LOL. What political price?
Are these infuriated base people suddenly going to vote for Trump in the fall? Yeah...not happening.

Some might. Some might have voted for Trump, even though he's worse on the issue than Biden from their eyes ("Hi, Uncommitted voters in MI who want to cut off their nose to spite their face!"). Still others would vote for a third party like Cornel West. And among the rest, there weren't any that would have started voting for Trump in the fall if Biden had used the powers in the bill, either - once the bill had passed, Biden would have had a free hand to gain votes from independents and centrists having already lost all of the progressive votes he was going to lose. In what world would he pass that up?

It's the same reason why Obama was "Deporter-in-chief" to his base during his administration. He was just better than Biden in recognizing earlier that it was an electoral liability to be perceived as out of center on immigration, and that the smart play was to keep the numbers manageable. Biden was slow to learn that lesson, but he had clearly learned it by early 2024.