* Thursday debt ceiling deadline approaching
* Reid says negotiations 'substantive'
* Offers little concrete information
* Fight could go down to wire
Senate negotiations to bring a boiling fiscal crisis to an end showed signs of progress on Sunday, but there were no guarantees that the U.S. federal government shutdown was about to end or that a historic default would be avoided.
Friday's optimism that a deal might be forged before financial markets opened on Monday vanished on Saturday and the talks moved from the acrimony of the House of Representatives to the Senate.
Negotiations that were likely to stretch into the week continued between the Senate's top Democrat and Republican.
Underscoring the urgency of resolving the impasse, both the Senate and House are scheduled to be in session on Monday, even though it is the Columbus Day federal holiday.
However, whatever deal the Senate might reach will still have to return for approval by the House, where the Republican majority faces strong pressure from its vocal conservative flank not to make any concessions to President Barack Obama and his Democratic Party.
Given that, hopes for forcing a conclusion before the Treasury reaches its debt ceiling on Thursday and runs out of authority to borrow may hinge in part on fear of tumbling investor confidence.
Financial markets began the week in Asia with a close eye on developments. U.S. stock index futures fell and the safe-haven yen rose broadly, foreshadowing a rocky start for Asian shares after the weekend failure to reach an agreement.
U.S. stock index futures fell 0.8 percent in early trade. If the losses are sustained, it indicates that Wall Street would open lower later on Monday.
U.S. stocks had risen strongly ahead of the weekend on hopes a deal to raise the $16.7 trillion federal borrowing limit was near. Failure to raise the debt ceiling would leave the world's biggest economy unable to pay its bills in the coming weeks.
On Saturday, House Speaker John Boehner informed his rank-and-file that the negotiations with the White House had collapsed. The focus moved to the Senate, which held a rare Sunday session with lawmakers delivering speeches about the prolonged standoff to an empty chamber.
Behind the scenes, Senate Majority Leader Harry Reid and Republican leader Mitch McConnell held conversations that Reid later called "substantive." Reid did not provide details. But if they bear fruit those talks could lead to a series of rapid legislative actions.
Reid's remarks capped a dreary Washington day that gave some hope that Congress soon might pass legislation to fund the government - in shutdown mode since Oct. 1 - and increase borrowing authority.
"I'm optimistic about the prospects for a positive conclusion to the issues before this country today," Reid said before closing the Senate for the day.
Earlier on Sunday, McConnell issued a statement calling on Democrats to accept a bipartisan plan that would end the government shutdown and raise the borrowing authority.
What started as a Republican effort to fight Obama's signature healthcare reform law by depriving it of funds and blocking a budget agreement has morphed into a stalemate on other issues.
"I don't even understand, at this moment, what this is about," said Democratic Senator Claire McCaskill, "It's not about Obamacare anymore. Is it about reforming Medicare and Social Security? That's not clear. Is it about how much money we're spending? That's not even clear. It feels like we're boxing shadows,"
Senator Dick Durbin, the second-ranking Democrat, boiled the fight down to just a couple of seemingly easy matters to resolve: the size of the increase in Treasury's borrowing authority and how much the government would be allowed to spend in a temporary funding bill after money ran out with the Sept. 30 end of fiscal year 2013.
Nonetheless, Democrats and Republicans jockeyed to win added provisions to those two basic issues, slowing the talks.
While McConnell urged Democrats to accept a bipartisan plan that has been developing for several days, some senators and their aides said that details were still being worked out on the very measure the top Republican was touting.
But if those discussions progress, the normally slow-moving Congress could kick into high gear.
In 2011, during the last major battle over the debt limit, a deal was announced the night of July 31 of that year. By Aug. 1, the House of Representatives had passed a bill; the next day the Senate went along and hours later, Obama had signed it into law.
Even so, the 2011 fight went right down to the wire and this year's battle seemed to be shaping up no differently. If a deal is reached, lawmakers could be voting on it as late as Wednesday or Thursday.
FOREIGN AND DOMESTIC CRITICS
As the acrimony continued, China's state news agency Xinhua called for an end to the "pernicious impasse" and said it was time for a "de-Americanized world."
China is among the largest foreign holders of U.S. debt.
In Washington, U.S. veterans' and conservative Tea Party groups protested the government shutdown, taking down barricades around the World War Two memorial on the National Mall before marching to the gates of the White House.
Police officers, some in riot gear, pushed back against the crowd when it got too close to the White House fence, creating a brief flashpoint of anger in an otherwise peaceful demonstration.
The rally included speeches from Sarah Palin, a hero of the Tea Party movement and former Republican governor of Alaska, and Ted Cruz, a freshman Republican senator who has crusaded against Obama's healthcare law.
Cruz played a key role a few weeks ago in stoking Tea Party fervor against Obamacare and encouraged conservative House members to hold out for major changes to the law even if it meant a partial government shutdown.
They have not won any changes to the law yet. But they won a government shutdown. Since then, House Republican leaders' efforts to broker a way out of the standoff failed, leaving senators to try to find a deal.
"Here's what I'm worried about," Republican Senator Lindsey Graham told ABC's "This Week," "a deal coming out of the Senate that a majority of Republicans can't vote for in the House."
House leaders spoke bitterly Saturday of the prospect of being "jammed" later this week: put in a situation by the Senate and possibly by market turmoil of having to rush something through at the last minute, probably with the votes of Democrats as well as the some of the Republican majority.