Adding this because I don't see it explained anywhere else:

It takes 60/100 votes to pass the budget bills in the Senate, instead of 51, because the Senate still has a filibuster. The minority Democrats have the power to stop the vote from coming up by simply talking on the floor forever until the Republicans give up and go home.

The 53-47 vote was for a cloture motion, which is to put time limits on debate on a particular budget bill. The rules don't let Dems filibuster the cloture motion for obvious reasons, so that vote happened. But it takes 60 votes to pass cloture, so it went down.

Now, there are some resolutions that don't involve coming to a compromise:

• the Democrats could choose not to do the filibuster. Then the bill would come up, and they could all vote against it, but it could pass on 53 votes.
• the Senate could change the rules to get rid of filibuster. This is usually called the "nuclear option" because it removes the 60 vote barrier using a rules vote that only needs 51 to pass. The procedure is to make someone actually start a filibuster, then raise a point of order that filibustering member is taking too long. The Parliamentarian will deny the point of order based on the current rules, but that can be appealed to the whole Senate on a majority vote. And the point of order is not debatable.

And since the GOP shits on everything left of far right atm, they get to be petty and maybe get some ground back. Plus last time around, the Dems had leverage and blew it spectacularly. Schumer wrote a strongly worded letter I believe. I feel bad for federal workers, but this government needs a rework anyhow. And not the technocratic, corpo, or fascist facelift some seem to yearn for.