Remember Embrace the Suck? It was Nancy Pelosi's way to urge Democrats to vote for the Budget Bill, even though it did not have extension of unemployment insurance. And not just Nancy Pelosi, but the the most progressive Democrats, "embraced the suck" and voted for the Budget bill. Not just the most progressive, but liberal heroes, like Bernie Sanders and Elizabeth Warren. At the time, this was considered the pragmatic thing to do, even though the budget also cut Federal pensions. On the other hand, the deal did restore some of the worst sequester cuts, e.g., to medical and scientific research.
I hesitate to second guess liberal lions and lionesses like Pelosi, Sanders and Warren. Pelosi earned a place in history for passing the ACA, (remember that the House even passed a public option version), just as Warren did for the Consumer Protection Agency.
But at that time in December, it was clear that a stand alone UI extension was going to be nearly impossible with the sociopaths roaming the House. It's pragmatic to try to figure out what will happen if you do or don't go along with something. If no budget had passed in December, those sequester cuts would still be with us, and there still would not have been UI extension. See the current FP piece on efforts in the Senate to extend UE.
And there would be a risk of another government shutdown. I think Dems were concerned that this time they would be blamed. I'm not sure that's true. Especially if the issue can be framed as the Republicans shutting down the government to stop continuation of unemployment insurance for millions (which is popular).
I'm a pragmatist too -- a perfect is the enemy of the good kind of guy in most situations. But part of pragmatism is knowing when to stop the expansion of the Overton Window when it renders the terrible (cutting off UE or food stamsp) acceptable.
That's the problem with "embracing the suck." It can lead to acceptance of the unacceptable.