Washington (CNN) -- With Republicans steadfast in supporting an indefinite extension of all Bush-era tax cuts, Democrats in the House and the Senate moved Thursday to limit the reductions, in full, only for families making $250,000 a year or less.

Senate Majority Leader Harry Reid announced on Thursday night that he was told a single unnamed Republican scuttled an agreement over a plan for several tax-related votes. Despite that, Democrats would go ahead and weigh in Saturday only on the two bills that many of their members supported.

Earlier in the day, the U.S. House of Representatives passed a measure 234-188 to allow tax cuts instituted under President George W. Bush to expire this December 31 for Americans' incomes above a quarter-million dollars annually.

The tax cuts for incomes below that would continue, and the bill would also maintain the current Alternative Minimum Tax limit for two years. Most Democrats backed the legislation, while Republicans resoundingly opposed it.

The Senate, per a deal reached by the chamber's Democratic and Republican leaders, was initially going to vote on that proposal, another that would raise the threshold to $1 million and the GOP-backed effort to indefinitely extend the cuts for all taxpayers as soon as Friday. But Reid said that plan fell through, and the Democrats decided to schedule votes only on their first two options.

None of the measures -- including the Republican proposal -- was expected to get the 60 votes that would be needed to end debate and vote on the bills themselves.

"We do not support giving tax cuts to millions and billionaires," said Reid. " We are disappointed that we couldn't show the American people anything."

All 42 Senate Republicans vowed Monday to prevent a final vote on any other legislative business in the lame duck session until Congress has "prevented the tax increase that is currently awaiting all American taxpayers."

President Barack Obama and top congressional Democrats say the estimated $700 billion the GOP tax cut extension would cost the Treasury would be fiscally irresponsible. Republicans contend that a failure to extend all of the cuts would hamper an already sluggish economy.

Negotiators from the White House and both parties on Capitol Hill are meeting behind closed doors this week to try to hammer out a compromise. Multiple congressional Democratic sources told CNN Thursday that, despite what was happening on the floor of the House, a deal to extend all of the cuts temporarily was getting close.

After the House vote, the White House issued as statement saying that "extending middle class tax cuts is the most important thing we can do for our economy right now" -- and denying that negotiators were nearing a deal.

"But, because Republicans have made it clear that they won't pass a middle class extension without also extending tax cuts for the wealthy, the President has asked Director Lew and Secretary Geithner to work with Congress to find a way forward," the statement said. "Those discussions started just yesterday and are continuing this afternoon. The talks are ongoing and productive, but any reports that we are near a deal in the tax cuts negotiations are inaccurate and premature."

House Speaker Nancy Pelosi ripped Republicans for pushing what she characterized as unfunded tax breaks for the wealthy while insisting that any further extension of unemployment benefits for lower-income Americans be paid for.

"This is so grossly unfair," she said. "Something is very wrong with this picture."

"Giving $700 billion to the wealthiest people in America ... does not create jobs," said Pelosi, D-California. There must be a "tax cut for middle-income people in this country. ... That is what we send to the (negotiating) table."

Several economic studies have indicated that the wealthiest people -- the top three percent who make more than $250,000 per year -- are more likely to invest tax cuts in stocks or other assets than to create jobs. And, Democrats point out, many large American corporations are posting record profits without sinking that money into payroll. Instead of spending money on tax cuts, they say, the money should be spent on actual jobs -- which, in turn, will bring businesses the customers they need to thrive.

"It's time that this country began to tax fairly and invest wisely," said Rep. Xavier Becerra, D-California. "It's time that this country acted sanely."

House Minority Leader John Boehner -- in line to become speaker when Republicans take over the House in January -- called the Democrats' vote political "chicken crap" that undermines the spirit of bipartisan tax negotiations now under way between the White House and congressional leaders on both sides of the aisle.

"This is nonsense," he said. "The election was one month ago. There are 23 months [until] the next election and the political games have already started."

"This bill is as misguided as it is futile," said Michigan Rep. Dave Camp, the top Republican on the tax-writing House Ways and Means Committee. It is "the wrong policy at the wrong time."

"You cannot help the job seeker by punishing the job creator," said Rep. Jeb Hensarling, R-Texas. "No taxes on nobody. It may be bad grammar but it's great economics."

Indications that a deal to extend all of the Bush tax cuts for two or three years fueled concern among some Democratic lawmakers that the White House will not fight hard enough to get Democratic priorities in return.

"The goose is cooked," said one senior Democratic source. "The question is what the larger deal is going to look like."

Democrats are hoping to squeeze out of Republicans a wish list of concessions, according to Democratic sources. They say that list generally includes: a lengthy extension of unemployment benefits without having to find offsets to pay for them; extending college tuition tax credits set to expire at the end of the year; extending so-called "make work pay" tax credits expiring December 31; and tax credits for businesses that hire unemployed workers.

"This is the first fight of 2012," said one Democratic source.

Another Democratic source said that by agreeing to a temporary extension of all of the cuts, Democrats are simply facing reality.

"No one wants to leave here without extending the tax cuts," the source said. "The question is what are we getting in return for doing that. I don't know how much of an appetite there is for a long and drawn out fight. The calendar is not our friend."

CNN's Alan Silverleib, Dana Bash, Deirdre Walsh, Evan Glass and Ted Barrett contributed to this report.