By Dana Ford and Josh Levs, CNN
(CNN) -- A last-ditch Senate compromise to avert the fiscal cliff appeared to be in jeopardy with House Republicans slamming the deal negotiated with the White House and demanding more must be done to cut spending.
The measure that sought to maintain tax cuts for most Americans but increase rates on the wealthy passed the Democratic-led Senate overwhelmingly early on Tuesday. But Republican frustration over deficit-reduction muddled prospects for final action in the GOP-controlled House.
"This is not a good deal," said Rep. Steve LaTourette of Ohio. "This is a sad state of affairs -- that we're going to take a bill that was passed on New Year's Eve by some sleep-deprived octogenarians that has very, very heavy on taxes and does nothing to cut spending, which is really part of the big problem that we have in the country."
House Republicans met for a second time on Tuesday to discuss the next steps on the fiscal cliff --- whether to consider the bill as written -- a so-called up or down vote -- or amend it and send it back to the Senate.
Majority Leader Eric Cantor, R-Virginia, told reporters that he did not support the bill as passed by the Senate, dealing a major blow to its chances in the House.
Time was crucial, however, as a new Congress is set to be sworn-in on Thursday. Congress would have to start the process anew if there is no action on the fiscal cliff by then.
Rep. Nan Hayworth, R-New York, said she was hopeful her party would "come up with an alternative, an amendment that we can present to the Senate."
"We were elected and then re-elected as a majority to bring the federal government to the right size, to respect every tax dollar," said Hayworth, who lost her re-election bid.
House Minority Leader Nancy Pelosi told reporters that Democrats were eager to see what Republicans would put on the floor.
"Up until now, (Speaker John Boehner) has said when the Senate acts, we will have a vote in the House. That is what he said. That is what we expect. That is what the American people deserve, so we look forward now ... to see what the timing will be for a straight up or down vote on what passed 89-8 last night in the United States Senate," Pelosi said.
Later she tweeted: "Strong majority of House Ds support bipartisan Senate bill ... Confident it will pass if @SpeakerBoehner allows up/down vote."
The Senate adjourned until noon on Wednesday.
Boehner has not yet indicated when a vote might happen. Following the first meeting with his membership, Boehner released a statement through his spokesman, saying that conversations with representatives will continue.
"The speaker and (Cantor) laid out options to the members and listened to feedback. The lack of spending cuts in the Senate bill was a universal concern amongst members in today's meeting," it read.
Not all congressional Democrats were happy with the proposal that would maintain Bush-era tax cuts that expired at midnight on Monday.
The Senate plan would maintain tax cuts for individuals earning less than $400,000 and couples earning less than $450,000. It would raise tax rates for those over those levels -- marking the first time in two decades the rates jump for the wealthiest Americans.
Sen. Tom Harkin, D-Iowa, complained that the deal "makes tax benefits for high-income earners permanent, while tax benefits designed to help those of modest means and the middle class are only extended for five years."
The bill temporarily extends certain tax breaks, such as the one for college tuition, while making new tax rates permanent.
President picks up bragging rights, breaks a promise
While the deal gives President Barack Obama bragging rights for raising taxes on the wealthiest Americans, it also leaves him breaking a promise.
Obama had vowed to raise tax rates for the top-earning 2% of Americans, including those with household income above $250,000, and individuals earning more than $200,000.
"What I'm not going to do is to extend Bush tax cuts for the wealthiest 2% that we can't afford and, according to economists, will have the least positive impact on our economy," the president said at a news conference in November, after being asked by CNN why Americans should believe he would not "cave again this time" by allowing those Bush-era tax cuts to be extended.
When asked whether closing loopholes instead of raising rates would be satisfactory, the president responded, "when it comes to the top 2%, what I'm not going to do is to extend further a tax cut for folks who don't need it, which would cost close to a trillion dollars. And it's very difficult to see how you make up that trillion dollars, if we're serious about deficit reduction, just by closing loopholes in deductions. You know, the math tends not to work."
The deal passed by the Senate would cap itemized deductions for individuals making $250,000 and for married couples making $300,000.
Raising the threshold for higher tax rates to $400,000 shrinks the number of Americans affected. While nearly 2% of filers have adjusted gross incomes over $250,000, only 0.6% have incomes above $500,000, according to the Tax Policy Center.
Still, in a written statement early Tuesday, the president held on to the 98% figure he has so often touted.
The deal "protects 98% of Americans and 97% of small business owners from a middle class tax hike," he said. "While neither Democrats nor Republicans got everything they wanted, this agreement is the right thing to do for our country and the House should pass it without delay."
The president also acknowledged, "There's more work to do to reduce our deficits, and I'm willing to do it. But tonight's agreement ensures that, going forward, we will continue to reduce the deficit through a combination of new spending cuts and new revenues from the wealthiest Americans."
However, many Americans are still likely to see their paychecks shrink somewhat, due to a separate battle over payroll taxes.
Senate vote 'sends a strong message'
"Glad it's over," said Senate Majority Leader Harry Reid, D-Nevada, after the vote on the fiscal cliff deal, just a couple of hours after the East Coast rang in the new year. "We'll see if the Republicans in the House can become functional instead of dysfunctional."
An early statement from House leadership made no promises.
"Decisions about whether the House will seek to accept or promptly amend the measure will not be made until House members -- and the American people -- have been able to review the legislation," the statement said.
Sen. John Hoeven, R-North Dakota, was hopeful the House will follow suit.
"The vote was 89 to 8. Bipartisan vote. 89 votes," he said. "I think it sends a strong message and I think it will be approved by the House."
What the package proposes
Under the Senate package:
-- Taxes would stay the same for most Americans. But they will increase for individuals making more than $400,000 and couples making more than $450,000. For them, it will go from the current 35% to the Clinton-era rate of 39.6%.
-- Itemized deductions would be capped for those making $250,000 and for married couples making $300,000.
-- Taxes on inherited estates will go up to 40% from 35%.
-- Unemployment insurance would be extended for a year for 2 million people.
-- The alternative minimum tax -- a perennial issue -- would be permanently adjusted for inflation.
-- Child care, tuition and research and development tax credits would be renewed.
-- The "Doc Fix" -- reimbursements for doctors who take Medicare patients -- will continue, but it won't be paid for out of the Obama administration's signature health care law.
-- A spike in milk prices will be avoided. Agriculture Secretary Tom Vilsack said milk prices would have doubled to $7 a gallon because a separate agriculture bill had expired.
What's not addressed
While the package provides some short-term certainty, it leaves a range of big issues unaddressed.
It doesn't mention the debt ceiling, and temporarily puts off for two months the so-called sequester -- a series of automatic cuts in federal spending that would have taken effect Wednesday. It would have reduced the budgets of most agencies and programs by 8% to 10%.
This means that, come late February, Congress will have to tackle both those thorny issues.
"We're going to have to deal with the sequester, that's true," said Sen. Max Baucus, D-Montana, "but look, this is better than nothing."
Reid said the agreement was a win for average Americans.
"I've said all along that our most important priority was to protect the middle class families," he said. "This legislation does that."
And maybe a bit more.
According to the U.S. Census Bureau, median household income in 2011 was $50,054, which is well below the tax cut threshold approved by the Senate.
If the bill doesn't pass
There's a lot at stake.
If the House doesn't act and the Bush administration's 2001 and 2003 tax cuts expire, broad tax increases will kick in, as will $110 billion in automatic cuts to domestic and military spending.
The nonpartisan Congressional Budget Office has predicted the combined effect could dampen economic growth by 0.5%, possibly tipping the U.S. economy back into a recession and driving unemployment from its current 7.7% back over 9%.
"This Congress unfortunately has been most known for a unwillingness to compromise, an unwillingness to come together to act on behalf of the American people," said House Democratic Whip Steny Hoyer. "Today is Jan 1st. Taxes will be going up on everybody in America if we don't act."