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The 20 members of the Senate Democratic Caucus have successfully hung together twice — first rejecting their own version of the budget, then the House of Delegates’ version, as Mr. Bolling has ruled that he cannot break tie votes on the budget. Republicans would need only one crossover to end the impasse. That’s not going to happen, Mr. Saslaw said.

“Nobody in our caucus is going to crack, OK?” he said. “Name five people in our caucus they ain’t gone to offering the sun and the moon. And they’ve all been told ‘no.’ “