Yes, under the Common law (And this has NEVER been repealed, just ignored for reason I mention below) adjacent land owners HAD to maintain any ROAD that ran along their property. This common law rule is the basis of why state and local government can REQUIRE you to maintain a sidewalk. Furthermore, you can NOT charge for the work it was your cost of having a public road along your property AND that public road is to be kept free for anyone to use.
In some states local governments (Texas for example) STILL charge homeowners whenever the road through their neighborhood is repaired. The Government does the repairs, and the home owners get to pay for it (Both for the sidewalks AND the actual road work done). When I was in Texas this was only done on local neighbor roads NOT major highways. The reason the local government does the work is it is cheaper for the local government to do such repairs, given it is being done on the whole street, then then if each homeowner had the repairs on the part of the road they are responsible for. The local Government can repair the entire road a lot cheaper then if each homeowner did it on they own, but the local government can then charge such home owners a proportional share of the overall costs, which can run up to a couple thousand dollars for each home owner.
Now, my home state of Pennsylvania does not DO this (i.e. charge homeowners for the repairs to the actual road) but there is NOTHING ON THE BOOKS MAKING SUCH FEES ILLEGAL, it is just not done (to many complaints from home owners once they get the bill for the "improvements"). Furthermore the State Government provides money to local governments to maintain their roads (less then what is needed but it is some help) and the local government know they can NOT collect twice for the same repairs (Once from the state and once from the homeowner) which is another reason you are NOT charged for such repairs.
Just pointing out that it is a courtesy of your local government that you do NOT have to not only repair and maintain your sidewalk but also the road itself. Furthermore the Common Law said it was a RIGHT OF WAY that anyone could use, thus you can NOT charge for any repairs, it is a cost of owner property next to a public road.
The problem of getting adjacent property owners to pay to improve and maintain a road came up when the States started to do improvements to the roads connecting the various cities before the railroads were built. The states would transform Public Roads into toll roads to pay for the improvements but to avoid the issue of prior free use these new toll roads tended to be a little off the old main roads (hereafter referred to as Mud Pikes), thus if you did not want to pay the toll, you could use the mud path that was the old road, or you could pay the toll and used the road bed with a hard surface that your wagon did NOT get stuck in every time it rained (I will avoid the problem with "Shun-pikers" local farmers who would build a dirt road around any toll both so to "Shun" having to pay the toll).
Now going on the old mud pike would cause some decline in fees on the toll road (as did shun-pikers), so most states ended up setting up tolls at choke-points (Generally River Crossings). At river crossings a bridge had to be built, as any bridge did NOT exist prior to the road construction (Most old mud pikes went to fords or ferries on the rivers) any one traveling on EITHER the then new Toll Road or the older public road had to cross the bridge (and pay the toll) or figure out another way to cross the river (Generally going on a ford or a ferry). Fords were dangerous, the current made you and your gear wet AND the animals wanted to get out of the water ASAP AND once out stop (Blocking the rest of the team from exiting the water, a dangerous mix, the first two animals wanting to stop, the next two RUSHING to get out of the water). It was worse if you had a herd, then the first animals would stop, and the rest of the herd would be rushing into them, leading to massive panic and drownings. Thus, if you had animals, either pulling a wagon or in a herd, you wanted to use a bridge, what you loss in paying the toll, you gain in avoiding losses in animals.
Given the above, the choke-points is where the money for tolls could be made and it was for this reason tolls survived on bridges for decades after toll roads on land had basically died out (Toll road died out in the 1850-1870 period, railroads became the main way to travel except for local traffic). Furthermore toll bridges re-appeared first as automobiles appeared after 1900 (Some toll bridges spanned both eras) and then as part of toll roads (Mostly in areas with no prior highways, so a toll could be charged and no one could claim prior free use).
Sorry about going in this tangent, but just wanted to make clear that the above statement as to road maintenance applied to existing roads at the time of settlement (Most were either Native American Paths slowly widened to accommodate pack horse, then wagons and then cars) OR designed as part of an urban design (and as such the roads and sidewalks were NEVER part of any lot OR if part of a lot, the lot was sold subject to the fact the lot owner not only had to maintain the sidewalk but also the road AND permit free use of such road and sidewalk). Toll roads could only be built on land NEVER used for any other purpose (Just like railroads were generally, but not always, built on right of ways that had NEVER been a public road). Being a "Private" road (i.e. private in the sense the public could NOT use it unless they pay for the right to use the toll road) the adjacent property owners had no duty to repair it, unlike public roads. As these toll roads died out, repairs were done by the state NOT the local land owners but only on these old toll roads.
With the advent of Gasoline taxes, it became common, again, for local and state government to maintain public roads (especially in urban areas) but as a courtesy NOT as a legal duty of the local Government. This first started in the 1880s as part of the bicycle craze, people wanted improved roads to ride their bicycle on (Yes, Gasoline taxes only started in the US in 1905, but the movement to improve roads re-started as part of the bicycle craze which quickly became tied in with the development of Rural Free Delivery which the Post Office, the Post Office insisted no Rural Free Delivery unless the area had some sort of "improved roads" i.e. all weather road). The need to improve Rural Roads could ONLY be implemented on a governmental level, most local farmers were NOT willing to pay to Macadamized (The cheapest way to improve roads in the 1800s) the road next to their property. Thus most road improvements had to be implemented on a local or governmental level (one of the reason my home state of Pennsylvania has so many small local units was in the period 1880-1920 many areas who wanted improved roads found such improvements blocked by others in their local township, so to get improved roads the people in the area that wanted improved roads would form a new township or borough so they could get the new local government unit to do such work, thus many of Pennsylvania's local governments started out as break away areas that wanted "improved roads" while the rest of the township did not).
The Macadamized process of Improved roads is used till this day (Now called "Chip and dip), for it was cheap and lasted a good long time, through NOT for high speed use. One needed specialized equipment to do the work, but it was NOT that expensive IF you did more then the part of the road next to any one farmer (i.e. on a local, County or State Government level NOT the individual level). Thus by 1900 most areas had gone to government paving roads, but as you can see it had less to do with any change in the underlying law then people willing to pay taxes to get the job done by the government. While people were willing to pay taxes to get the job done, no one ever made any change in the law that says the local, County or State Government HAD to maintain public roads (The courts have found local government liable for bad constructions and bad maintenance of roads but NOT for NOT contracting roads or maintaining them or even abandoning roads).
Side note: Urban roads were generally dirt till the late 1800s, when it became common to do a cheap pave job to keep the mud to a minimum. At the same time most urban areas were undergoing a Streetcar boom, the streetcars were being out on many urban streets to permit more rapid movement of people in the growing cities. Almost all cities required these streetcars, in exchange for the right to run streetcars on their streets, to upgrade the streets AND to keep them clean even in winter. This duty survived till the last streetcars were replaced by buses in the 1960s. The worse part was the streetcar part of the street had to be maintained by the Streetcar Company, any part of the street outside the part of the street the street car traveled was still to be maintained by the adjacent property owners. When such owners just neglected to do so (For the simple reason they took the streetcar to and from work) the urban areas took over such areas as the upper middle class (the group of American most likely to buy cars prior to WWII) used their political connections to get those areas maintained so they could drive their cars.
I can go on, but just wanted to mentioned the Streetcars and how streetcars changed people's idea of who was to maintain the streets were they home was on. Road Maintenance went from being done by the adjacent property owner to the local government in a Multiple step process, many occurring at the same time (Gasoline taxes, cars and Streetcars all becoming popular about 1900). It was NOT just one thing it was this combination (And the fact that the city could hire a crew with heavy equipment and do the repair cheaper then any one person could do such repairs himself). Thus it became the norm for City to maintain road ways, but to leave sidewalks up to home owners (Mostly do to the fact sidewalks could last decades do to a lack of heavy traffic, while roads may only last a few years before the weight of vehicles would tear up the road bed).
More on Macadamize road:
http://en.wikipedia.org/wiki/Macadam