President Barack Obama cut short his holiday and returned to Washington to try to hammer out a deal, as time is running short for legislators to come together on a comprehensive plan to address the changes slated to go into effect within a matter of days.
Reid said the government appears headed over the so-called fiscal cliff because of a lack of bipartisan co-operation.
"It looks like that's where we're headed," the Nevada Democrat said.
A series of tax cuts that have been extended several times are about to expire, resulting in an extra $536 billion for American taxpayers. At the same time, military and other spending budgets are slated to be cut by $110 billion.
The combination of those two moves, it's feared, will send the American economy tumbling back into recession. But the two sides can't agree on concessions to avoid that prospect.
Steny Hoyer, Democratic whip of the House of Representatives, said Thursday that he wanted to see the House working toward a solution. He told reporters that Americans were expecting substance from legislators as the crisis loomed.
Democrats, he said, were ready to work and ready to compromise as part of the effort to avert the fiscal cliff.
Later Thursday, Reuters reported that the House would hold a session Sunday night, citing a senior Republican aide. The Associated Press said it's not clear what legislation the House might consider Sunday, since Boehner is publicly insisting that the Senate must make the next move to avert the cliff.
Some legislators who are already back in Washington were beseeching each other to strike a balance.
In recent days, Obama's aides have been consulting with Reid's office, but Republicans have not been part of the discussions, suggesting that much still needs to be done to strike and pass a deal, even a small one, by Monday.
On Wednesday, Treasury Secretary Timothy Geithner sent a letter to congressional leaders warning that the government was on track to hit its borrowing limit on Monday, Dec. 31., unless a law is passed to extend the ceiling by another $200 billion or so to get through the next few months.
Geithner has said he would take "extraordinary measures as authorized by law" to postpone a government default, but he said uncertainty over the outcome of the fiscal cliff negotiations made it difficult to determine how much time those measures would buy.
Jan. 1 is not a hard and fast deadline. Congress could still act in January in time to retroactively counter the effects on most taxpayers and government agencies, but chances for a large deficit reduction package would likely be put off.
Taxes are a major stumbling block. Obama says he wants to come up with a way of extending some of the tax cuts to most Americans while letting taxes go higher for the wealthiest ones.
House Republican leaders on Wednesday urged the Democratic-controlled Senate to consider or amend a House-passed bill that extends all existing tax rates. "The Senate first must act," they said.
But Reid's office insisted that the Republican-controlled House act on Senate legislation passed in July that would raise tax rates only on incomes above $200,000 for individuals and $250,000 for couples.
Meanwhile, Obama has been pushing for a variant of that Senate bill that would include an extension of jobless aid and some spending reductions to prevent the steeper, broader spending cuts from kicking in.
Even if the Senate acts, Boehner would have to let the bill get to the House floor for a vote. The chances of accomplishing that by Dec. 31 seem slim.
Whenever the debt ceiling hits, however, it is likely to set up yet another deadline for one more budget fight between the White House and congressional Republicans.
House Republican leaders this week put the burden on Reid, urging him in a statement Wednesday to take up a House-passed bill that would extend current tax rates to all taxpayers, a bill Obama has vowed to veto.
Reacting to Reid's floor remarks Thursday, Boehner spokesman Brendan Buck said: "Harry Reid should talk less and legislate more if he wants to avert the fiscal cliff. The House has already passed legislation to do so."