In our constitution:
Amendment 10: "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people."
The power to shut down normal lawful operations or avoid obligations of our government is NOT delegated.
Hence: Nobody in our United States government has the power or right to shut down our government.
Republicans: We just don't pass a bill to vote or vote against it if the president does not want to sign it, or he can veto it. We have the right to do that and he does too.
Answer: Amendment 9: "The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people." --- Meaning: No, you can't do that if the result is a shutdown. You have to do everything in your power [even if you don't want to] to keep the government running for the people of the United States.
Republicans: What if we don't? --- Answer: (with a question or two, or three) Well, when you were sworn in to your office or mandate did you not swear an oath to support the Constitution? What does that mean to you, if anything? Does that not mean you will do what you solemnly pledged to do?