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Mr. Obama’s three principles for a bill include: bringing down rising costs of health care delivery; ensuring patients can choose their own plans and doctors; and making sure all Americans have access to affordable health care.

Rep. Dave Camp of Michigan, the ranking Republican on the Ways and Means Committee, said Mr. Obama must push Democrats “to make this a truly bipartisan effort,” or the July 31 deadline is unrealistic.

• Stephen Dinan contributed to this report.