Senators Portman and Schumer would largely end the taxation of those repatriated profits, instead imposing a light annual tax on overseas income, whether it comes home or not. That, they said, would end the incentive to leave profits abroad or reinvest them in overseas operations. Mr. Obama’s international tax plan would set that minimum overseas profit tax at 14 percent. The new proposal does not set a rate, but Mr. Portman said the administration’s was far too high.

Image Rob Portman, an Ohio Republican, has joined with Mr. Schumer on the effort. Credit... Gabriella Demczuk for The New York Times

As a bridge to that system, the senators — like the president — propose a one-time tax on overseas profits that would be “deemed” repatriated, whether or not they come home. “Deemed repatriation” in exchange for a “territorial” system that primarily taxes corporate income generated in the United States is a deal that big business is willing to accept, Mr. Portman said.

It is also one that could produce hundreds of billions of dollars in taxes for public works to improve the nation’s aging infrastructure. That is an idea that has gained currency in Washington as both the White House and Republicans drop talk of an increase in the federal gasoline tax. With Democrats raising pressure on Republican leaders to produce a long-term infrastructure and highway bill, advocates of the tax proposal say it will gain more steam.

“As we get closer to the deadline, people are going to realize this is the only alternative,” Mr. Schumer said on Wednesday.

The proposal also embraces what European nations have called a “patent box” — a lower business tax rate for income derived from intellectual property patents.

Much of the move to cut corporate taxes reflects scrambling to replicate actions by foreign trading partners that have eased business tax rates and sought to lure investment. For Democrats, the attraction of the plan will be infrastructure funding and the closing of loopholes that have encouraged business investment abroad, while even encouraging some companies based in the United States to reincorporate in lower-tax countries. For Republicans, the plan promises lower tax rates and a simplified system.

Republican leaders, however, are divided on how to proceed. Mr. McConnell would like to cobble together funding for a two-year highway bill that would push the tax reform debate into the next presidency, when he hopes that a Republican will occupy the White House. Mr. Obama has said any broad overhaul of the tax code should raise revenue for the government and must maintain higher tax rates on the rich.