“I think there’s a lot of flexibility in terms of some of my contacts and conservatives in terms of not making it totally offset,” he said. “Does it have to be fully offset? My personal response is no.”

The health care failure also makes the tax overhaul more politically complex as the fissures within the Republican Party have been laid bare. Mr. Trump followed Mr. Ryan’s lead and lost, making it more likely that the White House will try to steer the direction of tax legislation.

“I would be surprised given the health law debacle if the Trump administration sits back and lets Congress fashion the legislation without weighing in on the substance,” said Michael J. Graetz, a tax law professor at Columbia University. “That is one of the lessons that the administration will take from the failure of the health bill.”

It remains unclear whether Mr. Trump and Mr. Ryan are in agreement on taxes.

Since last summer, Mr. Ryan and Representative Kevin Brady of Texas, the chairman of the Ways and Means Committee, have been aggressively pitching a reform blueprint that includes a “border adjustment tax.” It would be a 20 percent tax on imports that, by making imports more expensive, would spur domestic production, they say. They think the plan would raise $1 trillion to compensate for the lower revenue that much lower tax rates would probably bring in.

Mr. Ryan and Mr. Brady are unlikely to simply hand over tax policy to the White House. Mr. Brady said on Sunday that getting rid of the contentious border tax provision would have “severe consequences” and that he hoped to produce a bill based on the House plan this spring that would be passed later this year.

Mr. Brady’s tax-writing committee is expected to convene a meeting about an overhaul on Tuesday.

“We have so much in common with the Trump administration, it wouldn’t make sense to have a separate tax bill from Secretary Mnuchin, a separate one from Gary Cohn, a third from whomever,” Mr. Brady said on Fox News, referring to the Treasury secretary, Steven T. Mnuchin, and to one of Mr. Trump’s top economic advisers. “Why not take the basis of the House plan?”