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Asked whether he would filibuster Mr. Hagel’s nomination, Mr. Cruz said in a statement that “we should do everything possible to ensure the Senate has the information necessary to make an informed decision.”

Robert P. George, who advised Mr. Cruz in the 1990s when he was at Princeton, said he is “not a bit surprised” by Mr. Cruz’s voting record. He described the senator as a “conviction politician” and someone who has always thought for himself.

“He considers what he thinks is right and will follow his conscience wherever that leads,” said Mr. George, founding director of Princeton’s James Madison Program.

The approach has won him kudos from conservatives and tea partyers — many of whom are warming to the notion that Mr. Cruz should run for president in 2016.

Others, though, say Mr. Cruz is turning into the sleeping giant of the Republican Party’s “just say ‘no’” crowd.

“He may be standing for principle, but the fact is he has proven to be an entirely irrelevant to the Senate to date,” said Jim Manley, a Democratic strategist and longtime senior aide in the Senate. “If I was one of his constituents, I would be demanding his salary back.”