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Those spending battles and other fights over health care, debt and the extent of Mr. Obama’s powers appear to have taken a toll on Mr. Boehner. In March 2011, he was less known but more liked. Now, three-quarters of those surveyed know who he is, and have turned more sour.

The top two names of the 22 surveyed by Quinnipiac, which specializes in political polling, were New Jersey Gov. Chris Christie and former Secretary of State Hillary Rodham Clinton, at 53.1 and 52.1 respectively.

“Former Secretary of State Hillary Clinton’s score is not surprising given her lengthy political career and especially strong support among Democrats and women,” said Peter A. Brown, assistant director of the Quinnipiac University Polling Institute. “But Gov. Christopher Christie’s rating is impressive given that his experience — less than four years as governor — pales compared to Mrs. Clinton’s resume.”

Mr. Brown said they were the only two of the 22 names surveyed that scored above 50, highlighting the lack of faith in the nation’s top politicians.

Mr. Christie, whom many Republicans expect to run for president in 2016, does well across the political spectrum. Among independents, he was the most popular.

Several others who might take a look at the 2016 primary race top Mr. Christie among Republicans. They include Rep. Paul Ryan of Wisconsin, who scores a 68.7 warmth rating, followed by Sen. Ted Cruz of Texas at 65.6 and Sen. Marco Rubio of Florida at 65.1. Mr. Christie is eighth at 59.8 among Republicans, which is better than Mr. McConnell, Mr. Boehner, Louisiana Gov. Bobby Jindal and Rep. Peter T. King, a New York Republican who has hinted that he may consider a presidential run.