House Speaker John Boehner will put up for a vote as early as Thursday a bill that would raise taxes on those who earn $1 million or more a year, a signal to the White House that Republicans are ready to compromise to reach a deficit-reduction deal.

The legislation, dubbed "Plan B" by House Republicans, is meant to provide a "second track" in the negotiations over tax increases and spending cuts as Boehner, R-Ohio, continues to negotiate a final deal with President Obama. While the plan is an about-face for Republicans who have refused to consider any tax increase, it's silent on the deep spending cuts Republicans are demanding.

The White House immediately rejected Plan B, saying it would never pass the Democratic Senate.

Still, if the Republican-run House can pass a tax increase on millionaires this week it would put pressure on Democrats to compromise on spending cuts or risk being blamed for failing to stop the so-called fiscal cliff, the massive tax increases and budget cuts that would hit on Jan. 1 unless lawmakers and the White House can reach a deficit-reduction deal before then.

"Taxes are going up on everyone on Jan. 1," Boehner said during a closed-door meeting with Republicans, according to aides. "They're baked into current law. And we have to stop whatever tax rate increases we can."

Boehner offered his proposal shortly after Obama suggested that he would give ground on the tax increases he seeks. The president pledged during his re-election campaign to raise taxes on those earning $200,000 or more a year, but said he would accept a deal that raises taxes on those earning $400,000.

Obama's offer also includes $1.22 trillion in spending cuts and would extend the nation's borrowing limit, known as the debt ceiling, for two years.

Republicans have been pressuring Obama to accept deeper spending cuts, including reductions in entitlement programs like Medicare. They dismissed his proposed cuts, saying they rely to much on accounting gimmickry.

Obama's most recent proposal includes a small change to Social Security that would slow the growth of payments to beneficiaries. Liberals immediately attacked the proposal as harmful to the elderly, but Republicans said it didn't go far enough in reducing spending.

Senate Majority Leader Harry Reid, D-Nev., rejected Plan B, which he said is the product of the "Tea Party agenda."

But many Tea Party-backed House lawmakers have softened their opposition to raising any taxes. Many now say they are willing to accept new taxes if Democrats offer substantial spending cuts and serious reforms to Medicare, Medicaid and Social Security, the drivers of the nation's massive debt.

"If there are real cuts and real reforms to entitlement spending, all of us would have to reconsider" tax increases, said freshman Rep. Raul Labrador, R-Idaho.

Sen. Lindsey Graham, R-S.C., told The Washington Examiner that Senate Republicans might agree to raise tax rates on those making less than $1 million if Democrats agree to substantial entitlement reform.

"The 30- and 40-year problem we face is from an explosion in entitlements," Graham said. "You're talking about a fiscal cliff today, but it will be a fiscal tsunami 30 years from now."