* Senate Democrat Reid says negotiations 'substantive'
* Offers little concrete information
* IMF's Lagarde warns of "massive disruption" to global economy
* Asian shares fall, safe-haven Japanese yen rises
* Thursday debt ceiling deadline approaching
By David Lawder and Tim Reid
WASHINGTON, Oct 13 (Reuters) - U.S. Senate negotiations to bring a fiscal crisis to an end showed signs of progress on Sunday, but there were no guarantees the federal government shutdown was about to end or that a historic debt default would be avoided.
IMF chief Christine Lagarde warned of "massive disruption" to the global economy if the U.S. debt ceiling, which will be reached on Thursday, was not lifted. That is when the U.S. Treasury runs out of authority to borrow money.
"We would be at risk of tipping, yet again, into recession," Lagarde said in an interview broadcast on NBC's "Meet the Press" program.
Friday's optimism that a deal might be forged over the weekend vanished on Saturday and the talks moved from the acrimony of the House of Representatives to the Senate.
Senate Majority Leader Harry Reid and Republican leader Mitch McConnell held talks that Reid later called "substantive". Reid did not provide details, but his remarks gave some hope that Congress soon might pass legislation to fund the government - in shutdown mode since Oct. 1 - and raise its 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.
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 concessions to President Barack Obama and his Democratic Party.
With time running out to reach a deal, MSCI's broadest index of Asia-Pacific shares outside Japan fell 1.1 percent on Monday while the safe-haven Japanese yen rose. The Tokyo stock exchange was shut for a public holiday.
U.S. stock index futures fell 0.7 percent to indicate a weaker opening on Wall Street.
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.
Banks and money market funds are already shunning some Treasuries normally used as collateral for short-term loans, a sign that a deadlock over the debt ceiling could disrupt a key source of day-to-day funding in the financial system.
CONGRESS COULD KICK INTO GEAR
On Saturday, House Speaker John Boehner informed his rank-and-file that negotiations with the White House had collapsed.
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.
Senator Dick Durbin, the second-ranking Democrat, boiled the fight down to 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 fiscal year-end.
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 had been developing for several days, some senators and their aides said details were still being worked out on the very measure the top Republican was touting.
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 down to the wire and this year's battle seems 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
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.
"The United States is the world's largest economy. We hope they can shoulder their responsibilities," said Hua Chunying, a foreign ministry spokeswoman, told a regular briefing on Monday.
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.
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. 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: a deal coming out of the Senate that a majority of Republicans can't vote for in the House," Republican Senator Lindsey Graham told ABC's "This Week".