The experience with the health bill suggests this will be a tough sell in the Senate.

Since releasing a one-page outline in April, the Trump administration has been offering mixed signals about its tax plan. According to a news report on the website Axios this month, Stephen K. Bannon, President Trump’s chief strategist, has been pushing for a tax increase on the rich in which the top individual rate would rise above 40 percent from 39.6 percent. However, Steven Mnuchin, the Treasury secretary, dismissed the idea this week and said the White House wanted to cut taxes for everyone.

Mr. Mnuchin has also recently walked back his promise from earlier this year that the wealthy would see no absolute tax cut under the tax legislation that Mr. Trump ultimately signs. Democrats had tried to hold him to the promise by calling it the “Mnuchin rule.”

Breaking that rule could be hard to avoid. A report released on Wednesday by the Tax Policy Center showed that Republicans might face a problem with overhauling taxes that is similar to the one they are facing with health care, with the policy benefiting those who are already the most prosperous. The tax research group analyzed the rough tax details that the Trump administration has released and found that 40 percent of the total $7.8 trillion tax cut would flow to the wealthiest 1 percent of all households.

One thing that could make the calculus easier for Republicans is simply abandoning their aspirations for tax “reform” and settling for tax cuts.

“I think that the dynamics of a bill that cuts benefits at the same time as it reduces taxes for others may be different from the dynamics of a bill that just cuts taxes,” said Itai Grinberg, a tax expert at Georgetown University’s law school.

The leftover Affordable Care Act taxes could also complicate the tax overhaul in procedural ways. One reason that Republicans chose to address health care first is that budgeting rules would allow them to make more sizable cuts to tax rates without adding to the deficit if the health taxes were already out of the way.

Even though some Republicans are disappointed that any taxes introduced by Mr. Obama remain, they will probably get another chance to erase them. Jonathan Traub, a tax expert at the accounting and consulting firm Deloitte and a former staff director for the House Ways and Means Committee, said Republican tax writers in Congress would be under pressure to find a way to address those taxes when they move on to tax legislation. Doing so outside the context of health care, Mr. Traub said, could be easier.