Whether the party can reconcile more demands of its base with the will of its leadership could determine how enduring the Republican Senate majority will be. The crop of senators up for re-election in 2016 includes those elected in the first Tea Party wave of 2010. And in a sign of what is at stake, even some of them are sounding notes of compromise and caution that would have been unthinkable at the height of the right’s resurgence.

“I understand the frustrations of the conservative base; I am one of them,” said Senator Ron Johnson of Wisconsin, one of the original class of Tea Party-inspired senators. “I also recognize reality.”

“We’re not going to pass the entire conservative agenda tomorrow. We can certainly lay it out,” Mr. Johnson added. “Let’s start with the things we can pass. Doesn’t that make more sense?”

But in a stark reminder of the difficulties Republican leaders will face from within their own ranks, other lawmakers popular with the Tea Party base are saying the fight is on.