With President Trump’s promise to repeal and replace the Affordable Care Act nearly dead, administration officials are scaling back their ambitions to cut the corporate tax rate sharply, apparently taking a more pragmatic approach as they scramble to secure a major legislative victory this year.

In recent days, discussions among Mr. Trump’s economic advisers over promised tax cuts for corporations and individuals have taken on new urgency, a person who has been briefed on the matter said. One crucial point of discussions in the coming days, the person said, will be the proposed business tax rate. In April, a White House policy paper pegged it at 15 percent for corporations and small businesses alike. The current rate is 35 percent.

But now the proposed business tax rate is “drifting higher,” this person said, and may end up in the low 20 percent range.

With the health care plan seemingly in ruins, this person said, the tax overhaul will very likely take top priority. Steven Mnuchin, the Treasury secretary, and Gary D. Cohn, the director of the National Economic Council, are communicating daily over the tax proposal with the aim of drafting a bill to be introduced on the House floor in early September. To ensure the support of influential lawmakers in both chambers of Congress, the two officials are meeting weekly to discuss the bill’s intricacies in a group being referred to as the Big Six: House Speaker Paul D. Ryan; Kevin Brady, the chairman of the House Ways and Means Committee; Mitch McConnell, the Senate majority leader; and Orrin G. Hatch, the chairman of the Senate Finance Committee.

The final tax rate will depend somewhat on whether corporations are permitted to deduct their interest expenses — a…