Updated: 11:49 a.m.

A Congressional Budget Office analysis released Wednesday morning found that the deficit cutting bill proposed by Senate Majority Leader Harry Reid (D-Nev.) cuts significantly deeper and faster than the one proposed by Speaker John Boehner (R-Ohio), although it still fell $500 billion less than the $2.7 trillion advertised.

Sources indicated, however, that Reid was already in the process of tweaking his proposal, which is why he has not yet begun the time-consuming procedural maneuvers needed to bring the measure to a vote in the Senate.

A Reid spokesman said Democrats are still gratified by the overall CBO assessment. “We are glad Congress’ budget referee agrees that the Senate bill cuts the deficit by $1.3 trillion more than Speaker Boehner’s bill. We are also glad to see that CBO credits the Senate bill with a full trillion dollars in savings from winding down the wars, rebutting Republicans’ arguments once and for all,” Adam Jentleson said. “It becomes clearer by the hour that the Senate bill is the only true compromise in Congress, so it’s time for Republicans to get serious about averting the economic crisis looming in less than a week and drop their doomed tea party bill.”

Much of the shortfall is due to the CBO scoring the package on its current, updated budget assumptions from March. That includes hundreds of billions of dollars in cuts already assumed because of the continuing resolution funding the government.

The same scoring trouble befell Boehner’s bill Tuesday, sending the GOP leadership back to the drawing board to meet its promise of a one-to-one match of spending cuts to increase the debt limit.

And the Reid score complicates the endgame for finding a deal to raise the debt ceiling before the Aug. 2 deadline set by Treasury Secretary Timothy Geithner to avoid a default on U.S. obligations.

The score found that Reid’s plan would slice the deficit by $2.2 trillion over a decade — with more than half of that coming from assumptions that the United States will wind down wars in Iraq and Afghanistan. The GOP has ridiculed using that presumed savings as a budget “gimmick.”

Still, even without the war assumptions, Reid’s bill cuts significantly more than Boehner’s and significantly faster, the CBO analysis showed. Before savings on interest on the debt, the discretionary spending caps in Reid’s plan cut $751 billion over the next decade versus $710 billion in Boehner’s original bill.

And in the first two years, Reid’s bill shrinks the deficit by $129 billion versus $17 billion for Boehner’s plan. Even without the war funding, Reid’s bill would slice the deficit by about $58 billion in the first two years — more than three times Boehner’s savings.