The nonpartisan Congressional Budget Office said that under the Democratic measure, deficits also would rise in each of the next two years before turning downward.
Democratic officials had said earlier in the day their bill would spread one year's worth of anticipated savings—$85 billion—over a decade in an attempt to avoid damaging the shaky economic recovery.
The legislation would cancel across-the-board cuts due to begin on Friday. Instead, it would eliminate payments to some farmers, enact defense reductions beginning in two years and impose tax increases, mostly on millionaires.
White House spokesman Jay Carney recently told reporters at the White House the administration supports the measure.
The Senate is expected to vote on Thursday on rival Democratic and Republican plans to replace the spending cuts, known in Washington-speak as a "sequester." Both bills are expected to fail.
In an indication that across-the-board cuts are inevitable, President Barack Obama has set a meeting with congressional leaders for the day they take effect. While the administration has warned of severe cuts in government services as a result of the reductions, few, if any, are likely to be felt for several weeks.
That could give the administration and lawmakers breathing room to negotiate a replacement, although Senate Republican Leader Mitch McConnell said during the day there were limits to what could be negotiated.
"We can either secure those reductions more intelligently, or we can do it the president's way with across-the board cuts. But one thing Americans simply will not accept is another tax increase to replace spending reductions we already agreed to," he said.
Democrats said their proposal to replace across-the-board cuts was designed with the economy in mind.
It "seeks the same amount of savings in a more responsible way" as the $85 billion in cuts that will otherwise take effect, said Adam Jentleson, a spokesman for Senate Majority Leader Harry Reid.
"The impact on the economy is much better. Sequestration as constituted would hurt economic growth and destroy jobs," he added.
Over a decade, the bill would cut deficits by an estimated $110 billion, half from higher taxes and half from the defense and farm program cuts.
That is in keeping with Obama's call for a balanced approach that combines selected spending cuts with closing tax loopholes.
Senate Democrats have been reluctant to spell out the details of their measure, although it is not clear if that results from its relatively small impact on the deficits through the end of the current budget year.
Across the Capitol, though, the party's leaders have talked openly of their desire to spread the cuts in their replacement measure over a longer period.
"It is entirely intentional," said Rep. Chris Van Hollen, D-Md., and the party's senior member on the House Budget Committee. "The whole idea is to achieve the equivalent deficit reduction without hurting jobs and having disruption in the economy. You do that by having targeted cuts and eliminating tax loopholes over a longer period of time," he added.
He said the Democrats' approach is the same as Federal Reserve Chairman Ben Bernanke's recommendation, which is to help the recovery gain strength before beginning to make cuts.
In the Senate, Republicans have yet to disclose their own sequester replacement measure. Most of the rank and file favors an alternative that lets Obama adjust the cuts to minimize any impact on the public, but that approach has its critics among lawmakers who fear giving the White House that much authority.
AP White House Correspondent Julie Pace contributed to this report.