If the Dems are loud and united, proclaiming they will not vote for reducing taxes on the wealthy and corps, without substantial middle-class cuts, and it appears true, they'll be fine if they hold it up.
They actually did a reasonable job earlier, presenting the Medicaid healthcare cuts as "funding" for wealthy tax cuts, causing the GOP to back-off a bit.
Now if they don't deliver the message, they can be hurt. But I don't think that will happen; they're messaging is getting decent enough in certain things, like healthcare. I'm thinking this might be the same.
I also think there's a unique facet at play here. Trump won the election in large part by stealing away the working-class base from the Dems. If the tax cuts are seen as a giveaway to the rich and the corps, at the expense of the working-class, and the Dems run with that, they might jam-up Trump.
This might be their chance to resume their fight for the working man, and calling-out Trump as "a billionaire plutocrat skewing the tax code to himself and the plutocratic Republican elites". So I think Trump can be pressured here, if the tax code is mostly a rich man's giveaway, and if the Dems play their cards right. That's "if".