But some Republican senators who helped write the bill, along with influential business groups who support it — including the U.S. Chamber of Commerce and the Business Roundtable — have started a countereffort to try to persuade House Republicans to back the legislation.

“It’s a good bill; it’s right there for the country, so I’m encouraging Republicans to support it,” said Senator Rob Portman, Republican of Ohio and one of the bill’s negotiators, who said he was working the phones hard. “There’ll be some that have told me they will, but they’re under a lot of pressure.”…

A few House Republicans who are members of the bipartisan Problem Solvers Caucus have announced their support for the measure, including Representatives Tom Reed of New York, Brian Fitzpatrick of Pennsylvania and Don Bacon of Nebraska. On Monday, Representative Don Young of Alaska, the longest serving member of the House, announced his support with an impassioned speech on the House floor.

Moderate Democrats say others may follow suit — maybe as many as 20 Republican votes — if Ms. Pelosi can win over enough liberals to keep it close. But with a Thursday vote looming, time is running out.