A decision by one or all of them to try to bolster their standing with Republican-leaning voters in their states by backing the president’s nominee would undermine Democratic leaders as they try to sustain party unity. And if their votes put the president’s choice on the court, it could hasten the move to the left by the party’s aggressive activist core, while intensifying the clamor for new, more confrontational leadership.

But if they hold together on a “no” vote, those senators could not only surrender their own seats, but by expanding the Republican majority, they could also narrow the path of Democrats to a Senate majority for years to come by ceding those states to Republicans.

“It is a terrible vote,” Jennifer Duffy, a longtime nonpartisan analyst of Senate races for the Cook Political Report, said about the showdown, which will escalate on Monday with the scheduled official announcement of the nominee.