WASHINGTON, Oct 7 (Reuters) - The U.S. Senate on Thursday began a procedural vote aimed at trying to pass a stop-gap increase in the Treasury Department"s $28.4 trillion borrowing authority as lawmakers rushed to stanch worries about a debt default in less than two weeks. That came after hours of debate on the bill that would raise the debt limit by $480 billion - enough to keep Treasury borrowing and spending humming through at least early December. If the legislation clears that first hurdle to limit debate on the bill, as expected, the Senate would then be poised to vote on raising the debt ceiling to $28.9 trillion. If the Senate cannot agree on speeding up the steps toward passage, the debate could spill into Friday or the weekend. "We have reached agreement to extend the debt ceiling through early December and it"s our hope we can get this done as soon as today," Democratic Senate Majority Leader Chuck Schumer said earlier on Thursday. News of the negotiations drove Wall Street"s main indexes to end sharply higher in a broad-based rally. In a sign of bond market relief, the yield on one-month Treasury bills fell to its lowest point since Sept. 8 as investors deemed that risk of default had eased. There were early signs of resistance from some Republicans who registered opposition to either the bill itself or the procedures for debating it. Gaining enough Republican cooperation to promptly move forward on the bill, No. 2 Senate Republican John Thune told reporters, "will be a painful birthing process." If the Senate approves the bill, the Democratic-led House of Representatives would then vote on the measure before it went to President Joe Biden to sign into law. RECONCILIATION Washington"s debt limit troubles are unlikely to be resolved even with passage of the short-term increase. Top Senate Republican Mitch McConnell is still expected to insist that the next increase in December be achieved through the "budget reconciliation" process that is time-consuming but will allow for passage without any votes from his party. Doing so could bolster Republican candidates in the 2022 congressional elections as they try to burnish their credentials as fiscal conservatives - even though most of them previously supported an array of measures passed during Republican Donald Trump"s administration that jacked up U.S. budget deficits. Democrats have adamantly rejected using the reconciliation process - which they have turned to to pass some of Biden"s other priorities - in this case as too unwieldy and establishing a bad precedent. Referring to the deal providing a debt limit reprieve until December, McConnell said in a Senate speech: "Now there will be no question. They"ll (Democrats) have plenty of time" to pass the next increase using reconciliation. Democrats had been trying to pass legislation that would have raised the debt limit through the end of 2022, which Republicans blocked. Without congressional action, the Treasury Department has forecast that it will run out of ways to pay all of its bills and meet its debt obligations by Oct. 18. While the deal relieves debt ceiling pressures for now, it adds to the high-stakes, partisan battles Congress will wage through the end of the year. Democrats want to pass two massive spending bills that make up much of Biden"s domestic agenda in the coming weeks, including a multitrillion-dollar social policy package to be passed by reconciliation and a $1 trillion bipartisan infrastructure bill. It also faces a deadline for funding the government beyond Dec. 3. The partisan debt limit fight raised Republican fears that Democrats might change a rule known as the filibuster that requires a supermajority of 60 votes for most legislation to advance if the debt issue were not resolved. The 50-50 split in the Senate has allowed Republicans to use the filibuster to block several Democratic initiatives. Biden said late on Tuesday that Democrats would consider making an exception to the filibuster to hike the debt ceiling and defend the economy. Reporting by Susan Cornwell, David Morgan and Makini Brice; Writing by Richard Cowan; Editing by Scott Malone, Sonya Hepinstall and Rosalba O"Brien Our Standards: The Thomson Reuters Trust Principles.