In almost any other government shutdown, Senators Tim Kaine and Mark Warner, both of Virginia, would probably top the list of Democrats most likely to try to find a quick off ramp.

They represent the state with the second-highest concentration of federal employees in the nation. Both have historically been eager to join the so-called bipartisan gangs of senators who try to negotiate their way through partisan gridlock.

Instead, the two have appeared remarkably dug in, even as President Trump and his top lieutenants have threatened to use the shutdown to drastically accelerate their campaign to reduce the size of the government. They say they are channeling federal workers who are furious at the White House’s ongoing assault on the bureaucracy and are urging their representatives in Congress to keep up the fight.

“I’ve heard that sentiment more loudly than I thought, because in Virginia, we have an awful lot at stake,” Mr. Kaine said in a recent interview. “We suffer more in a shutdown scenario than anybody else. But I think they feel like, ‘You’re threatening to hurt us. You’ve been hurting us since Jan. 20.’ In some ways, it’s kind of not a credible threat, because you’ll do it anyway, whatever happens.”

The dynamic has fueled Democrats’ resolve not to back down as the shutdown impasse drags into its second week. Democrats representing large populations of federal workers have for months heard from livid employees about the Department of Government Efficiency emails they received asking them to provide a list of accomplishments; the chaos and upheaval at their agencies; and the fears of retaliation.