I believe that the vast majority of Americans would strongly support maintaining these programs at current levels and the pressure would be on Republicans to support these programs. In other words, put up or shut up.

But the CR did that! It maintained the funding for those programs at current levels! It didn't change the funding for those programs. It's a continuing resolution - it just continues existing levels of funding. That's why the whack-jobs on the far right of the GOP caucus (like Massie and Roy) had to have their arms twisted to vote for it. Because they didn't want to continue Biden levels of spending and wanted cuts to lots of programs, and Trump told them they had to get in line. The programs you're talking about were maintained at current levels.

That's why the Democrats were going to get crushed if the shut the government down over this. There >b>were things in the bill that they claimed (perhaps correctly) made it not a "clean" CR - some extra border enforcement and defense funding, a few billion in cuts to domestic programs - but nothing that could realistically be explained to voters as a reason for fighting the CR.

That's why Schumer went along with it. This was a trap! The GOP passed a CR that didn't do anything significant to current funding levels and dared the Democrats to vote against it in the Senate. The Democrats wanted to add stuff to the CR to reign in DOGE, and they might have had a chance (though doubtful) to do that if the bill had died in the House. But it didn't, and the GOP always had 50+ votes in the Senate for the CR, so the Dems were done for - they couldn't blame the GOP for not having the votes to pass their own bill, which meant they'd take a bunch of the blame for the shutdown.

This was the CR, not the budget bill. That will have a lot of cuts and changes which the Democrats can attack....but that's going through reconciliation, so the GOP doesn't need any Dem votes in the Senate if they can agree amongst themselves.