Republicans have fired back by accusing Democrats of political grandstanding and saying it is their refusal to fund adequate border protection that has caused the military to be penalized.

“They play politics with everything,” Ms. McSally said on Tuesday, dismissing the criticism from Democrats and defending her support for the declaration even though a military project in Arizona was on the Pentagon’s list of cuts. “I support border security,” she added. “And I also support our military, and I think we should be able to do both.”

Mr. Tillis, who initially said he would vote against Mr. Trump’s emergency declaration but ultimately changed his mind and supported it, said Democratic criticism did not bother him.

“I’m not really concerned with it,” Mr. Tillis said. “Our record will speak for itself — not worried about the short-term distraction.”

Republicans cannot dodge the issue, since the law Mr. Trump invoked to declare the emergency allows a vote to terminate it to occur every six months. The resolution is not likely to bring about an end to the declaration, however, unless a surge of Republicans switch positions to distance themselves from the president, an unlikely prospect given their staunch refusal to do so on other issues.

To Democrats, that is the point. They believe the vote will underscore how closely Republicans are allied with Mr. Trump even at the expense of home-state concerns, a position that they believe will hurt incumbent Republicans with the independent voters that will be crucial in 2020.

“If Democrats can use this vote with independents, I think it could be particularly powerful,” said Nathan Gonzales, a nonpartisan congressional race analyst and editor and publisher of Inside Elections. “This will give Democrats another piece of evidence that these senators are too close to the president.”