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It’s not that Republicans whom conservatives deride as “Republicans in name only” don’t talk and vote conservatively. Many of the House Republican leaders whom conservatives consider to be too moderate have strong conservative voting records.

Few debates are surer to grow into heated arguments than betting that House Speaker John A. Boehner, who last year narrowly won a second term as speaker, has a liberal record. In fact, the Ohio Republican had a 90 percent American Conservative Union lifetime voting rating before he became speaker. The ACU gives a 96 rating to House Majority Leader Eric Cantor of Virginia and a 94 rating to Majority Whip Kevin McCarthy of California.

Senate Minority Leader Mitch McConnell, a Kentucky Republican facing a fierce tea party challenge in his primary race this year, has a 90 percent ACU lifetime rating. The Senate’s second-ranking Republican, John Cornyn of Texas, can boast of a 93 ACU voting score.

Their critics, however, say it’s on unrated procedural votes and inside maneuvering that the McConnells and Cornyns differ from Mr. Cruz and allies such as Sen. Rand Paul, Kentucky Republican. Those differences lead to compromises that, to Republicans like Mrs. Van Etten, give everything to Democrats.

“Republicans are taking a big risk doing that because it can turn off their base and cause [voters] to stay home this fall,” she said.

Not everyone agrees with the hard line against compromise.

Lynn A. Stout, a distinguished law and business professor at Cornell University, argues that Republicans take even bigger risks by not compromising at tactically important times, even if many in the party base perceive capitulation.

From her Ithaca, N.Y., office, Ms. Stout said “some compromise is necessary to prevent Republicans from losing influence, especially with young voters.” She said polls generally show that using lost-cause filibusters such as Mr. Cruz’s attempt to defund Obamacare last fall is “a damaging strategy to Republicans.”

Sen. John McCain of Arizona, the party’s 2008 presidential nominee, has accused Mr. Cruz of instigating last year’s partial government shutdown and called the Texan “crazy.”

Thermostat Republicans note that Mr. McCain and other critics of the Cruz filibuster failed to put any of the blame for the shutdown on Mr. Obama and Senate Democrats by rejecting bill after bill to carry on government operations during the standoff.

Mitt Romney, the party’s presidential nominee in 2012, pointedly left Mr. Cruz and Mr. Paul off the list in November when he was asked to list the best available Republicans to head the ticket in 2016.

Of two minds

Former Virginia Gov. James S. Gilmore III, who served as RNC chairman and now heads the Free Congress Foundation, said his own career shows the conflicting impulses of thermostat versus thermometer politics.

Mr. Gilmore has played the Republican thermostat in his political career by standing up to President George W. Bush’s administration, for example, on foreign interventionism and government surveillance programs.

But Mr. Gilmore is of two minds on mounting hopeless fights in Congress over a principle. He faults Mr. Cruz, Mr. Paul and their allies for their tactics last fall.

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