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Sen. Richard G. Lugar, Indiana Republican, credited the president with reaching out to Republicans in hopes of striking a deal.

“My understanding is that the meetings that President Obama has had have certainly had an element of reaching out,” he said Sunday on CNN’s “State of the Union.” “And I think that has been appreciated.”

Mr. Lugar also acknowledged that Mr. McConnell must deal with some conservatives who seem to oppose the president on every issue, and he cautioned fellow Republicans that their party must never become “the party of no.”

He also cautioned Democrats about their use of the lame-duck session, saying his colleagues want an assurance that the session would be limited to tax legislation, a broad spending measure and a Strategic Arms Reduction Treaty with Russia. If Republicans get that assurance, he said, the pact can pass with “strong bipartisan support.”

“The votes are there,” said Mr. Lugar, who also is ranking Republican on the Senate Foreign Relations Committee.