Crucial details of the House and Senate versions of the plan are still unknown, in part because Republicans are struggling with how to pay for the tax cuts they are envisioning. Lawmakers have cleared the way for a $1.5 trillion tax cut but are considering a plan that would cost much more than that, which will require them to find a way to offset the cuts by ending tax breaks and employing accounting maneuvers to stay within that defined amount.

Many of the details still in flux are important because they would affect middle-class taxpayers directly, including the boundaries of income-tax brackets, the size of an expanded child tax credit and the fate of some deductions that Republicans had targeted for elimination, such as one for state and local taxes paid.

A framework for the plan, released by Republican leaders in September, calls for cutting corporate rates; nearly doubling the standard deduction for individuals and couples; reducing the number of individual income tax brackets to three or four, from seven; overhauling the way in which the United States taxes multinational corporations; and taxing so-called pass-through entities, which are businesses whose owners pay taxes on profits through the individual tax code, at a rate of 25 percent.

Depending on how the details are filled in, such a tax bill could reduce income taxes on nearly all middle-class families — or it could raise them for millions of middle-class families, by eliminating deductions and other tax breaks and not reducing rates enough to make up for that.

Publicly, Republicans have long said Democrats should — and will — vote for their tax bill. Mr. Trump has sought to pressure, in particular, a handful of Democratic senators from states he won, including Joe Manchin III of West Virginia, Heidi Heitkamp of North Dakota and Joe Donnelly of Indiana.

Mr. Trump invited several Democrats to the White House this month, along with every Republican on the Finance Committee, and placed Senator Claire McCaskill of Missouri, another Democrat from a state he won, next to him at the table. Before the meeting, Mr. Trump joked that he expected to get “unanimous support” from Democrats on the bill.

The Democrats left pleased with the president’s talk. “He said all the right things there,” said Senator Sherrod Brown, Democrat of Ohio, who delivered copies to Mr. Trump of two tax bills focused on the middle class that he is sponsoring. “He said, over and over, this is a middle-class tax break; this is not for rich guys like me.”