Other possibilities included temporarily suspending some excise taxes, such as the 7.5 percent tax airlines pay to the Federal Aviation Administration; increasing community development block grants; and fixing an error in the 2017 Republican tax overhaul that makes it more expensive for restaurant owners to do renovations.

Mr. Trump previewed several ideas at a news conference on Monday evening, but discussions remain in flux and many of the proposals would require congressional approval at a time of deep partisan ire and with the 2020 election looming.

The idea of a payroll tax cut in particular has divided Mr. Trump’s advisers, with Mr. Mnuchin and Larry Kudlow, the director of the National Economic Council, expressing concerns about the cost, whether it would address the problems caused by the virus and what Democrats would demand if they reopen the tax code.

However, Peter Navarro, Mr. Trump’s trade adviser, has been a proponent of the idea, and Mr. Trump has been pushing for it to be included in a package of options.

Mr. Navarro has often been at odds with Mr. Trump’s other economic advisers over trade policy. His appearance with the coronavirus task force at Mr. Trump’s White House briefing on Monday raised eyebrows among some officials who wondered if he had inserted himself into the fiscal stimulus discussion.

Mr. Navarro said in an interview that he was there at the president’s request.

“The president specifically asked during the Oval meeting that I, by name, and other members of his economic and trade team stand with him on the podium, and I left when the president left,” Mr. Navarro said.

Leaders in the Democratic-controlled House have also reacted with skepticism to the payroll tax plan. They have pushed for the administration instead to ramp up spending on the public health response to the virus.