(CNN) — A possible "bright day" in the U .S. Senate could mean a long day in the House.
Senate leaders from both parties say a deal is near to end the partial government shutdown and avoid a potential default as soon as this week.
However, House Republicans decided Tuesday to offer their own proposal that would tack on provisions changing President Barack Obama's signature health care reforms in what appeared to be a last-gasp effort to influence the agreement to reopen the government and raise the federal borrowing limit.
According to GOP sources and confirmed by Republican Rep. Darrell Issa of California, the House plan would include most of what is in the Senate agreement while adding a provision to suspend an Obamacare tax on medical devices for two years and remove federal health care subsidies for Obama and legislators when they obtain health coverage under the reforms.
In addition, the House proposal would forbid the Treasury from taking what it calls extraordinary measures to prevent the government from defaulting as cash runs low, in effect requiring hard deadlines to extend the federal debt ceiling.
Issa said a House vote could occur as soon as Tuesday night, while Senate Majority Leader Harry Reid indicated Monday that his talks with GOP counterpart Mitch McConnell could yield an agreement during the day.
Reid said Monday night that the negotiations with McConnell made "tremendous progress" toward an agreement, raising hopes among investors, world leaders and regular Americans that the shutdown stalemate was nearing an end.
"Perhaps tomorrow will be a bright day," he said.
U.S. stock futures -- often seen as an indicator of how markets will open -- were up only slightly early Tuesday as investors largely waited out the politicians.
Obama spoke Monday with McConnell, according to a GOP Senate aide, but the White House canceled a planned meeting with congressional leaders in what was perceived as a move to give Reid and McConnell room to negotiate.
Sen. Bob Corker, R-Tennessee, said it was time to get a deal done after lengthy delays he blamed on the unrealistic goal of gutting Obama's signature health care reform law.
"The fact is we've got to figure out a way to move ahead," he told CNN's "New Day" on Tuesday. "In fairness, on our side of the aisle, we've wasted two months, focused on something that was never going to happen."
However, the House GOP decision to offer a counter-proposal promised further delay toward final congressional action on an agreement.
The negotiations are also being closely watched by other nations, which would also feel the impact should the United States run out of money to pay some of its bills.
Jon Cunliffe, who will become the deputy governor of the Bank of England, told British lawmakers over the weekend that banks should begin planning for contingencies.
The partial shutdown -- now in its 15th day -- has proved costly. Hundreds of thousands of federal employees are either idle at home or not being paid for their work during the shutdown. Government offices, many parks and other facilities are closed. And officials warn that tough choices are ahead about which bills to pay and which to let slide, should the shutdown and debt ceiling debate drag on.
So far, the standoff has cost the economy about $20 billion in gross domestic product, CNN's Christine Romans reported Tuesday on "New Day," citing Mark Zandi of Moody's Analytics. GDP is a measure of the goods and services produced by an economy.
At a visit Monday to a local food pantry, Obama warned of what he called continued partisan brinkmanship by House Republicans who "continue to think that somehow they can extract concessions by keeping the government shut down or by threatening default."
"My hope is a spirit of cooperation will move us forward over the next few hours," he said.
The finer points
Reid and McConnell have to reach a resolution on two critical issues: ending the partial government shutdown that began on October 1 and raising the debt ceiling so the U.S. can borrow more money to pay all the government's bills.
Democrats want an increase in the debt ceiling to last for several months, to avoid similar showdowns in coming months.
At the same time, they want a spending plan to reopen the government, but one that will be temporary. This will allow them to work toward a longer-term agreement that can negate the effects of the forced sequestration cuts.
Republicans want the opposite.
They want a longer spending proposal that would lock in the planned sequestration cuts in coming months. And they want a shorter debt ceiling extension in order to negotiate further deficit reduction measures.
"We'll get this done. We're going to get this done. I feel real confident," said Sen. Joe Manchin, D-West Virginia.
'Solve this problem today'
At his visit to the Martha's Table food pantry in Washington, Obama said the congressional leaders could "solve this problem today."
He warned that a default -- in which the government would lack enough cash on hand to pay down its debt obligations, as well as other daily bills such as Social Security checks -- "could have a potentially devastating effect on our economy."
"We've already had a damaging effect on our economy because of the shutdown," he said. "That damage would be greatly magnified if we don't make sure that government's paying its bills, and that has to be decided this week."
The Treasury Department has said it will be unable to pay the government's bills unless the debt limit is increased by Thursday.
Democratic sources told CNN that the proposal under consideration by Reid and McConnell would fund the government through January 15, allowing it to reopen for at least three months or so.
At the same time, negotiations on a budget for the full fiscal year would have a deadline of sometime in December, the sources said.
Meanwhile, the debt ceiling would be increased through February 7 to put off the threat of default for almost four months, according to sources in both parties.
The budget negotiations were expected to address deficit reduction measures and therefore could affect when the debt limit would need to be increased again.
In addition, provisions involving Obama's signature health care reforms could be included, such as strengthening verification measures for people seeking federal subsidies to help them purchase health insurance required by the 2010 Affordable Care Act, the sources said.
Another possible change to the health care reforms would delay a fee on employers, unions and other plan sponsors that raise money to compensate insurance companies for taking on high-risk customers in the early years of Obamacare.
CNN political analyst John Avlon said Monday that Democrats wanted to press what they perceive as an advantage over Republicans on how the public regards the latest round of Washington budget and deficit brinkmanship.
"What's behind it (are) poll numbers that saw Republicans getting their butt kicked because of this whole gamesmanship," Avlon said.