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The Senate plan, he said, violates one of the central promises Mr. Obama made in that speech by adding $250 billion to the national deficit.

“So far the president has let Democratic leaders in Congress basically run the show to the exclusion of any constructive Republican suggestions, which I think could be a way out of this in a way that would actually reduce the costs and make health care more accessible to more people, which ought to be our focus,” Mr. Cornyn said.

Mr. Pence said Republicans’ messaging effort mirrors the coordinated approach they took during the debate over the president’s budget, which they said “spends too much, taxes too much and borrows too much.” Though Democrats passed the $3.6 trillion proposal, Mr. Pence said, the strategy was successful.

He said House Republicans have “the highest degree of unity” on health care, which he credited in part to an active August recess.

Asked whether Republicans were engaging in tactics they have previously described as fear-mongering - notably, when Democrats warned that efforts by the George W. Bush administration to reform Social Security would harm seniors - Mr. Pence said it’s “about educating the public.”

“Abraham Lincoln said, ‘Give the people the facts and the Republic will be saved,’” he said. “This is really about making sure they understand the real implications of what Obamacare will mean to them and their families.”

Tom LoBianco contributed to this report.