Congressional aides predicted Majority Leader Harry Reid and Republican leader Mitch McConnell could seal an agreement on Tuesday, just two days before the Treasury Department says it will run out of borrowing capacity.
The emerging pact would reopen the government through Jan. 15 and permit the Treasury to borrow normally until early- to mid-February, easing dual crises that have sapped confidence in the economy and taken a sledgehammer to Republicans' poll numbers.
"The general framework is there" between Reid and McConnell, said Republican Sen. Bob Corker. He said conversations with the House were continuing and that he thought it would be midday Tuesday at the earliest before a plan was finalized.
Many House conservatives were unhappy about the emerging framework, though it remained to be seen whether they would seek to change it.
The US stock market turned positive on the bullish predictions about the outcome of the Reid and McConnell negotiations.
The Dow Jones industrial average, which had risen strongly late last week on hopes of an agreement, rose another 64 points Monday.
Asian stocks rose slightly tracking the rise on , with Japan's Nikkei 225 adding 0.2 percent in early trading Tuesday.
The partial government shutdown, which has furloughed 350,000 federal workers, began on Oct. 1 after Congress failed to pass a bill temporarily funding the government.
Separately, if Congress doesn't approve a measure increasing the amount of money the government is allowed to borrow, the Obama administration says it will not be able to pay its bills, risking a default that experts say could prove catastrophic for the economy.
The plan under consideration by Reid and McConnell is a far cry from the assault on President Barack Obama's signature health care reform law that hardcore conservative tea-party Republicans originally demanded as a condition for a short-term funding bill to keep the government fully operational.
It also lacks the budget cuts demanded by Republicans in exchange for increasing the government's $16.7 trillion borrowing cap.
Nor does the framework contain any of a secondary set of House Republican demands like a one-year delay in the health care law's mandate that individuals buy insurance.
Instead, it appeared likely to tighten income verification requirements for individuals who qualify for subsidies under the health care law and may repeal a $63 fee that companies must pay for each person they cover under the big health care overhaul beginning in 2014.
Democratic and Republican aides described the outlines of the potential agreement on condition of anonymity because the discussions were ongoing.
But with Republican poll numbers plummeting and the country growing weary of a shutdown entering its third week, Senate Republicans in particular were eager to end the shutdown - and avoid an even greater crisis if the government were to default later this month.
Any legislation backed by both Reid and McConnell can be expected to sail through the Senate, though any individual senators could delay it.
But it's another story in the House of Representatives, where it wasn't winning a lot of fans among conservatives.
Republican Rep. Joe Barton signaled that conservative members of the House were deeply skeptical. He said any bill had to have serious spending cuts for him to vote to raise the debt ceiling and that he thought Obama and Treasury Secretary Jacob Lew had more flexibility than they had said publicly.
"No deal is better than a bad deal," Barton said.
Asked whether the emerging package contained any victories for Republicans, Rep. James Lankford, a member of the House Republican leadership, said, "Not that I've seen so far, no."
McConnell briefed House Speaker John Boehner on Monday on the status of the Senate talks. Both House and Senate Republican leaders scheduled closed-door meetings of their respective memberships for Tuesday.
As the Senate opened for business Monday, Reid said he was "very optimistic we will reach an agreement this week that's reasonable in nature."
Moments later, McConnell seconded Reid's assessment.
"We have had an opportunity over the last couple of days to have some very constructive exchanges of views about how to move forward," McConnell said.
"Those discussions continue, and I share (the) optimism that we're going to get a result that will be acceptable to both sides."
In addition to approving legislation to fund the government until late this year and avert a possible debt crisis later this week or month, the potential pact would set up broader budget negotiations between the Republican-controlled House and Democratic-led Senate with one goal being to ease automatic spending cuts that began in March and could deepen in January, when about $20 billion in further cuts are set to slam the Defense Department.
Democrats were standing against a Republican-backed proposal to suspend a medical device tax that was enacted to help fund the health care law.
Democrats also were seeking to preserve the Treasury Department's ability to use extraordinary accounting measures to buy additional time after the government reaches any extended debt ceiling.
Such measures have permitted Treasury to avert a default for almost five months since the government officially hit the debt limit in mid-May, but wouldn't buy anywhere near that kind of time next year, experts said.