A day before President Obama and congressional lawmakers were scheduled to meet to begin negotiating a plan to avert the so-called fiscal cliff, the top House Democrat signaled the party may be willing to accept a plan that does not raise tax rates, or would raise them only slightly.

House Speaker Nancy Pelosi, D-Calif., said Thursday that she supports Obama's proposal to allow the Bush-era tax cuts to expire for the nation's top two income brackets, beginning with couples earning more than $250,000 annually. But Pelosi signaled she is open to alternative ways of raising revenue, including a GOP plan that would close some tax loopholes or, alternatively, a plan to raise rates on top earners only slightly, in order to strike a "grand bargain" to avert the fiscal cliff.

"I'm fairly agnostic about certain things," Pelosi said. "I just want to have something that is fair and that will work."

In the Senate, meanwhile, some Republicans said they are willing to consider all proposals, even tax increases that they have publicly opposed.

"The last thing we need is for either side to be drawing lines in the sand," Sen. Bob Corker, R-Tenn., told The Washington Examiner.

Congress must scramble to strike a deal in the next few weeks that will prevent $1.2 trillion in automatic, across-the-board cuts as well as a tax increase for all income levels. Without a deal, the Congressional Budget Office has warned, economic growth would stall, and unemployment would rise to more than 9 percent.

Obama on Friday plans to meet with Republican and Democratic leaders at the White House in what has been billed as the opening round of talks. Both sides are expected to toss out proposals, including the GOP's plan to close loopholes rather than raise rates.

Under the president's proposal, tax rates for families with incomes greater than $250,000 would increase to 36 percent from 33 percent. Investment income would also be taxed at a greater rate -- rising to 20 percent from 15 percent.

Pelosi and Obama said they want a deal to result in the top 2 percent of earners paying more in taxes and said polls indicate a majority of Americans support such a plan.

But Republicans say increasing taxes on the top earners would hurt small businesses and eliminate hundreds of thousands of jobs. The GOP also is balking at President Obama's new request that the fiscal cliff deal produce $1.6 trillion in new revenue, twice the amount the president asked for during similar talks in the summer of 2011.

Senate Minority Leader Mitch McConnell, R-Ky., on Thursday said increasing revenue to $1.6 trillion would result in 20 cents in cuts for every dollar in new revenue.

"In other words, no cuts at all," McConnell said. "It's a joke, a joke."

House Speaker John Boehner, R-Ohio, who is meeting daily with his leadership team to construct a plan, has said he does not support a proposal to raise any tax rates.

Some of the more fiscally conservative House lawmakers, however, fear Boehner is "talking tough now" but will eventually cave in out of fear the GOP will be blamed for blocking a deal and sending the nation over the fiscal cliff, a congressional source said.

Not so, Boehner spokesman Kevin Smith told The Examiner.

"GOP leaders are in lockstep, working together to avert the fiscal cliff without raising tax rates," he said.