How do you "hold them to it"?

By campaigning on it, constantly. There's no other way. Elections have consequences. Democrats put up terrible candidates with a record of promoting unpopular policies and lost to Trump. Again!

See the Deciding to Win document:
Politico: F

I do agree this has gone on too long. And that this is even an issue is astounding. We seem to have this battle every six months, instead of forcing Congress to pass an actual budget. Don't let them go home until they do, recesses be damned.

Absolutely agree. Is part of their job to make sure the government is functioning? They aren't doing that. Congress' job rating is at 15%. How is it even that high?
news.gallup.com - Congress job rating sinks trump steady

I have doubts about the "football" theory. But maybe some bonehead thought that was a good approach for that reason? I don't see any advantage to it. I figured it was some sort of compromise that wouldn't raise the ire of too many voters.

It was probably due to the reconciliation process. They have to find savings to offset extra spending. Like the recent cut taxes/cut Medicaid dance.

But still, you get my point - Democrats are upset that Republicans won't extend a benefit the Democrats introduced. And almost every Democrat thinks the Republicans have shut down the government. I can't even...