As Majority Leader Harry Reid convened the U.S. Senate at midday Sunday, his Republican counterpart said a debt deal was within reach. Minority Leader Mitch McConnell, R-Ky., said on CNN\'s \"State of the Union\" he was \"very, very close to being able ... to recommend to my members that this is something that they ought to support.\" McConnell said the deal might not include any tax increases, something the majority Democrats had been insisting on as a means of chipping away at the budget deficit rather than relying solely on cuts to social programs. The halls of Congress were busy Sunday morning as lawmakers debated a compromise bill that would avert a federal debt default Tuesday. Reid, D-Nev., said the upper house would convene at noon and vote at 1 p.m. on a compromise bill hammered out Saturday, The Washington Post reported. \"Today is obviously a critical day,\" presidential adviser David Plouffe told NBC\'s \"Meet the Press\" as Wall Street powers warned of a stock market shock as soon as Monday if major progress is not made Sunday. Plouffe again dismissed speculation that President Barack Obama would invoke the 14th Amendment to force payment of debts if Congress fails to lift the ceiling by Tuesday. The Senate plan would raise the country\'s $14.3 trillion debt limit by up to $2.4 trillion in two stages -- $1 trillion now, matched by cuts, and the rest in 2012 unless two-thirds of both houses disapprove, the Post said. Without steering legislation, the United States will be unable to meet most of its financial obligations after Tuesday, The New York Times said. Reid told a news conference the latest bid to end partisan bickering came as a result of talks between McConnell and Vice President Joe Biden. McConnell said his package includes a vote on a balanced budget amendment to the Constitution before raising the debt ceiling but no requirement that it pass, as in the House Republican proposal. Sen. John Thune, R-S,D., said on \"Meet the Press\": \"This is probably going to be as good of an outcome as we can get, and most of us are going to have to accept things that we don\'t like in the final product.\" Sen. Claire McCaskill, D-Mo., said: \"Let\'s get away from the situation where the people who have power in Washington don\'t have to pay any taxes.\"