STORY HIGHLIGHTS
- NEW: A GOP source says the House is likely to vote on some version of the deal Tuesday night
- House Majority Leader Eric Cantor does not support the Senate compromise
- Other GOP representatives say more must be done to cut spending
- Lawmakers are under a tight deadline; A new Congress will be sworn in Thursday
With the fiscal cliff deal in limbo, what's your New Year's message to Washington? Go to CNN iReport to share your video.
(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."
The Senate bill would raise roughly $600 billion in new revenues over 10 years, according to various estimates.
Blog: Read the latest updates from CNN's political team
House Republicans met on Tuesday to discuss the next steps — whether to consider the bill as written -- a so-called up or down vote -- or amend it and send it back to the Senate.
Republican leaders gauged support for adding an estimated $300 billion in spending cuts, according to GOP sources. Those reductions, however, would be delayed for two months.
If approved, that plan would require additional action by the Senate, which adjourned until Wednesday.
The other option was to pass the Senate bill as written.
Time was crucial, however, as a new Congress is set to be sworn-in on Thursday. Congress would have to start over with votes if there was no action on the Senate bill or any other proposal by then.
The legislation as writtren now would avert much of the fiscal cliff's negative near-term economic impact by extending the Bush-era tax cuts for the majority of Americans. It would also extend long-term unemployment benefits that were set to expire.
If the House doesn't act and the tax cuts enacted last decade expire fully, 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 and possibly tip the United States into recession.
Global financial markets watched developments in Washington closely. Wall Street, which was closed on Tuesday due to the holiday, rallied on Monday on prospects that a deal finally would be approved by a bitterly divided Congress.
"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."
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.
But not all congressional Democrats were happy with the proposal. Liberals, especially, believed it was not tough enough on the rich.
Read more: 5 things to know about the fiscal cliff
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 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.
The proposal would temporarily extend 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.
Going over the fiscal cliff: Messages to Washington
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."
Obama 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.
What the Senate proposes
Read the bill (pdf)
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 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.
Read more: 3 more fiscal cliffs loom
CNN's Ed Payne, Matt Smith, Mike Pearson, Jessica Yellin, Dana Bash, Deirdre Walsh, Lisa Desjardins, Ted Barrett and Ashley Killough contributed to this report.
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