WASHINGTON  Republican Congressional leaders on Tuesday rejected President Obama’s challenge to come up with a single comprehensive proposal to achieve his goal of guaranteeing health insurance for nearly all Americans.

But they said they would attend a televised forum to discuss the issue with Mr. Obama on Thursday, even as they voiced doubt that he and Congressional Democrats were acting in good faith.

The Senate Republican leader, Mitch McConnell of Kentucky, and the House Republican leader, John A. Boehner of Ohio, made clear that they had extremely low expectations for the six-hour session.

“We will be at the meeting on Thursday and anxious to participate in the discussion,” Mr. McConnell said. “But it appears as if the administration has already made up their mind.”