Capitulate? That sounds like rhetoric that somehow blames democrats for the state of this mess, but the truth is that there aren't enough democrats in congress for them to matter.
There's enough republicans in the House of Representatives for a vote amongst party lines to pass a budget there. That's not a problem for them
There's also enough republicans in the Senate to make it happen with a simple majority, which they posess. They surely know this.
Republicans can end the debate and vote on a bill -- including one that can temporarily get things moving -- any time they want to. They've got the numbers to do that.
It's not a theory. There's precedent. They've made that shift previously[1] in the not-so-distant past.
[1]: https://en.wikipedia.org/wiki/Nuclear_option