General Discussion

I'm unsure what "tie breaker" you're referring to. Republicans refuse to even hold a vote on restoring ACA subsidies.

Motivations certainly enter into every political calculation and decision.

Republicans have been highly motivated to destroy the "Welfare State" for generations, and they're finally accomplishing that with Trump and Project 2025.

Each of them are also highly motivated to sustain and advance their political careers. Defying Trump means getting primaried in the next election, and perhaps getting death threats from the crazy MAGA base.

Of course, what's happened in the last 9+ months isn't playing well in public perception. Trump's approval is at 40% or less, and R's got trounced in last week's election.

The above three paragraphs are conflicting motivations. Only the last argues in favor of cooperating with Democrats -- but there has been no sign of that, except the meager concession on government employees to end the shutdown. If the shutdown continued and the unexpected happened with both the Senate & House restoring ACA subsidies (which I highly doubt) would Trump sign it -- even if they defied him by passing the legislation? He doesn't care if people starve or die for lack of healthcare (and neither do the R's for that matter). Everything is about his ego, greed, and whatever impulses go through his increasingly demented skull (or put there by Stephen Miller).

I suppose it's possible Republican strategists will conclude they have a better chance of holding onto the House if they concede some small victories to the Democrats. More likely they will do everything they can at voter suppression, and stealing elections. Trump and Miller, of course, are itching to find any pretext (or make one up) to send in the troops and seize ballots. I have no doubt this authoritarian regime has every intent to render elections as meaningless as in Putin's Russia.

Stopping that has to be the highest priority. Perhaps an indefinite shutdown would have served that purpose better, but a lot more suffering and destruction of government agencies would have been the price.