Speaker John A. Boehner of Ohio struggled Wednesday to find the votes for anything that would prevent the country from going over the fiscal cliff.

With both Democrats and hard-line conservative Republicans vowing to tank his “plan B” bill that would allow tax increases on millionaires, Boehner’s test Thursday will be to show the White House and Democrats that he has some control over his unruly conference as time to produce a deal averting tax hikes and automatic spending cuts runs out.

Boehner was confident Wednesday, telling reporters at a terse news conference that the House would pass a bill to extend the 2001 and 2003 tax rates for those making less than $1 million a year.

“The House will pass legislation to make permanent tax relief for nearly every American — 99.81 percent of the American people,” Boehner said at the hastily called news conference, during which he did not take any questions. “The president will have a decision to make: He can call on Senate Democrats to pass that bill or he can be responsible for the largest tax increase in American history.”

Behind the scenes, however, members were asking that spending cuts be part of any legislative package, including the speaker’s plan B. And leadership aides said the final package was still up in the air.