White House and congressional negotiators will come together on a deficit-cutting plan in time to avert a government default, the U.S. Treasury secretary said. "Despite what you hear, and this is a complicated place, Washington, people are moving closer together," Timothy Geithner told CNBC as White House officials and congressional leaders scrambled to devise a scaled-down proposal that would get both President Barack Obama's signature and enough Republican votes to pass the House. Geithner said he was "absolutely" confident a deal would be reached. Obama held a secret meeting Sunday morning with House Speaker John Boehner, R-Ohio, and Majority Leader Eric Cantor, R-Va., to come together on the possible shape and size of an agreement and how they could also possibly pull together a major deficit-reduction deal at the last minute, The Wall Street Journal reported. When asked about the meeting Monday, Obama said, "We're making progress." The meeting was originally intended to be just between the lawmakers and White House Chief of Staff Bill Daley until Obama dropped in, the Journal said. The latest plan draws from a plan advocated by Senate Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky., to allow the debt ceiling to be raised in return for about $1.5 trillion in spending cuts over 10 years. The difference is that the new version would give House Republicans ownership of the plan, a move that could make it more salable to GOP members, the Journal said. White House spokesman Jay Carney told reporters: "We have to ensure that there is a fallback provision, that there is a measure through which Congress will act and we can ensure that the United States will not default. And the leaders in that room are unanimously in support of doing that." The White House has said all sides need to reach a deficit-reduction deal by Friday to give Congress time to vote on raising the government's $14.3 trillion borrowing limit by Aug. 2. That is when Treasury Department officials say without more borrowing authority, the government will run out of cash to pay its bills, with possibly catastrophic effects on financial markets and the economy. Aware of the tight time frame, White House and top congressional leaders drew up a proposed timeline for getting a debt-limit bill passed by both houses in time. The timeline calls for the Senate to unveil its bipartisan plan this week and begin considering it Saturday, The Washington Post reported. The Senate could pass the plan by July 29, giving the House four days to consider whether to approve the plan before Aug. 2, the Post said. Before any of this happens, House Republicans plan Tuesday to vote on a bill to amend the U.S. Constitution to require a balanced federal budget. The so-called Cut, Cap and Balance Act has strong support in the Republican-controlled lower chamber, but is not expected to pass the Democratic-controlled Senate. Obama said Monday he would veto the measure should it pass Congress. Even though the measure will likely not become law, Republican leaders say that if they let the rank and file vent their frustration and vote for the deficit-cutting plan, that could clear the way toward passing a compromise before Aug. 2, The New York Times reported.