Union leaders have repeatedly warned the White House about the strong rank-and-file dismay, which could hurt the Democrats in Congressional elections this fall, especially in battleground states like Ohio, Pennsylvania and Wisconsin.

Ron Gay, an AT&T repairman in Youngstown, Ohio, who spent much of the summer of 2008 urging co-workers to vote for Mr. Obama, said, “If this passes in its current form, a lot of working people are going to feel let down and betrayed by our legislators and president.”

The Congressional Budget Office estimates that 19 percent of workers  or about 30 million employees  would be affected by the tax in 2016. Economists say most of them would be nonunion, although it is organized labor that has the lobbying clout to take a stand.

In recent days, labor’s strategy has become clear. Unions are urging their members to flood their representatives with e-mail messages and phone calls in the hope that the House will stand fast and reject the tax. The A.F.L.-C.I.O., a federation of nine million union members, has declared next Wednesday “National Call-In Day” asking workers to call their lawmakers to urge them not to tax health benefits. The International Brotherhood of Teamsters is urging members to tell their representatives that “such a tax is simply a massive middle-class tax hike that this nation’s working families should not be forced to endure.”

Many Democrats fear that enacting the tax will hurt their re-election chances.

“This would really have a negative impact on the Democratic base,” said Representative Joe Courtney, Democrat of Connecticut, who has enlisted 190 House Democrats to sign a letter opposing the tax. “As far as the message goes, it’s a real toughie to defend.”

While union leaders would prefer killing the tax, some say privately that they could live with it if the threshold is lifted to $27,000, say, or $30,000. They argue that many insurance policies above $23,000 are typical of the coverage in high-cost areas like New York or Boston, or policies that cover small businesses or employers with older workers.

Image An A.F.L.-C.I.O. ad warned union members that it believed voting for Senator John McCain in 2008 would be a mistake. Credit... David Maxwell for The New York Times

According to a union survey, one in four members would be hit by a $23,000 threshold, but only one in 14 if the threshold were raised to $27,000.