WASHINGTON — Senators Mitch McConnell and John Cornyn, two Republican leaders facing primary challenges, knew they would take an immediate political hit from the Republicans’ Tea Party wing by voting to clear the way for a debt-limit increase. They also knew that their willingness to cast that vote would enhance their party’s chances of gaining a majority in the Senate next year.

“It was not an easy exercise, but it keeps the focus on the issues we want it to be on,” said Senator John McCain, Republican of Arizona, who argued that by putting the debt limit fight behind it last week, his party had robbed Democrats of an opportunity to portray Republicans as reckless. “We dodged a bullet here.”

Democrats acknowledge that the Republican retreat on the debt issue was politically wise and represents yet another factor in the mounting concerns over their own Senate prospects. Democrats are counting on bursts of political extremism to wound Republican candidates. The move by Mr. McConnell, of Kentucky, and Mr. Cornyn, of Texas, showed that at least some Republicans have learned from past defeats.

“They seem to want to be on their best behavior in an election year,” said Senator Richard J. Durbin of Illinois, the No. 2 Senate Democrat.