Updated from 1:51 p.m. ET with market close information, an updated forward P/E ratio for JPM, and more on the federal debt limit debate in Washington. NEW YORK ( TheStreet) -- The nation's largest banks led a broad stock market rally Thursday afternoon, as Republicans in Congress appeared ready to come to an agreement with President Obama to raise the federal debt limit. The broad market staged a major rally, with the broad indices all ending with gains of more than 2%. The KBW Bank Index ( I:BKX) was up 3% to 63.30, with all 24 index components ending with gains of at least 2%. Big banks showing gains of over 3% included Capital One ( COF), with shares closing at $70.59, and State Street ( STT) of Boston, which closed at $66.94. Over the past week, investors have been fixated on the partial shutdown of the federal government that began on Oct. 1, because of the inability of the Republican-led House of Representatives and the Democrat-led Senate to agree on a continuing resolution to keep the entire government running. More importantly, investors have worried about the possibility of the United States defaulting on debt payments, if the legal federal debt limit is not raised above the current $16.7 trillion. U.S. Treasury secretary Jack Lew has previously warned the government could run out of money after Oct. 17. During testimony before the Senate Banking Committee on Thursday, Lew said the government has "large payments to Medicare providers, Social Security beneficiaries, and veterans, as well as salaries for active-duty members of the military," adding that a failure to raise the debt ceiling by Oct. 17 "could put timely payment of all of these at risk." Rep. Paul Ryan (R., Wash.) on Wednesday proposed a short-term increase of the debt limit, in order to allow time for a major agreement with Democrats to be negotiated, which "drew broad support from conservatives at the Capitol Hill meeting," according to a Wall Street Journal report. The Associated Press reported that House Speaker John Boehner (R., Ohio) also supported a short-term debt-limit increase. White House Spokesman Jay Carney told reporters Thursday that Obama would "likely sign" a clean bill to raise the debt limit temporarily. House Republican leaders were also expected to meet with Obama late Thursday afternoon. The positive developments raising hope of a timely solution to the debt-ceiling fiasco followed a positive reaction Wednesday to the president's nomination of Janet Yellen to chair the Federal Reserve after current Fed Chairman Ben Bernanke steps down in January.