WASHINGTON — Just two weeks from an economy-threatening deadline, fiscal cliff talks hit a lull Tuesday as House Speaker John Boehner announced that Republicans would also march ahead with their own tax plan on a separate track from the one he’s been pursuing with President Barack Obama.

The White House and leading congressional Democrats immediately rejected Boehner’s “Plan B,” which would extend soon-to-expire Bush-era tax cuts for everyone making less than $1 million but would not address huge across-the-board spending cuts that are set to strike the Pentagon and domestic programs next year.

“Everyone should understand Boehner’s proposal will not pass the Senate,” said Senate Majority Leader Harry Reid (D-Nev.).

Boehner’s surprise move came after significant progress over the past several days in talks with Obama — talks that produced movement on tax rate hikes that have proven deeply unsettling to GOP conservatives and on cuts to Social Security benefits that have incensed liberal Democrats.

Just Monday, Obama offered concessions, including a plan to raise top tax rates on households earning more than $400,000 instead of the $250,000 threshold he had campaigned on. And the two sides had inched closer on the total amount of tax revenue required to seal the agreement. Obama now would settle for $1.2 trillion over the coming decade while Boehner is offering $1 trillion.

By contrast, protecting income below $1 million from a hike in the top tax rate from 35 percent to 39.6 percent would raise only $269 billion over the coming decade.

But the outlines of a possible Obama-Boehner agreement appeared to have shaky support at best from Boehner’s leadership team and outright opposition from key Republicans like vice presidential nominee Paul Ryan (R-Wis.), a House GOP aide said. That aide spoke only on condition of anonymity because the aide was not authorized to discuss the situation publicly.

Though Obama spokesman Jay Carney had nothing good to say about Boehner’s new option, he said, “The president is willing to continue to work with Republicans” toward a broader agreement.

The narrower Plan B faced plenty of opposition. Democrats announced they would oppose it, and many conservative Republicans continued to resist any vote that might be interpreted as raising taxes. Republicans were refining the measure Tuesday in hopes of building support among the GOP rank and file, but passing the measure exclusively with GOP votes could prove difficult.

“I think it’s a terrible idea,” said Rep. Raul Labrador, (R-Idaho). “For a lot of reasons.”