Under the U.S. Constitution, there's a minimum requirement for passing a new law or changing an old one. You get a majority in both houses of the legislature, and consent of the President as executive. If the Senate thinks it's very important, you need a supermajority there (Currently, the Senate seems to think that very important=almost everything.) If the President objects, you need a 2/3 majority in both houses. Even so, a law that passes can later be declared unconstitutional by the judiciary.
At this time, the Republicans in the House of Representatives are proposing an exception to the above going forward: that as long as a party with a majority in only one house wants something badly, they can refuse to pay for any non-mandated spending, in hopes that everyone else will give them what they cannot get through the regular constitutional process.
Whatever you may think of our current Constitution, with its potential for gridlock and lack of clear accountability, the House Republican variation is much worse.