Mr. Cornyn said he was taking a page from Senator Charles E. Schumer of New York, the last head of the Democratic Senatorial Campaign Committee, who led his party to big gains by embracing candidates who, for example, opposed abortion rights or gun control.

“If you think about it, Schumer has been very good at this; I complimented him this morning in the gym,” Mr. Cornyn said, adding, “Some conservatives would rather lose than be seen as compromising on what they regard as inviolable principles.”…

Senator Jim DeMint of South Carolina said ideological purity was the road to success. “The best way to get to 60 is to have a core group of Republicans who really do what they say and stand for their principles,” Mr. DeMint said.