Updated: 7:56 p.m.

The Congressional Budget Office delivered the bad news to Speaker John Boehner (R-Ohio) on Tuesday evening that his deficit reduction proposal cuts just $1 billion from the deficit next year, sending staffers scrambling to rewrite the legislation.

Boehner spokesman Michael Steel said House Republicans are reworking the bill to make sure spending cuts exceed any increase in the debt limit.

“We’re here to change Washington: no more smoke and mirrors, no more ‘phantom cuts,’” Steel said. “We promised that we will cut spending more than we increase the debt limit, with no tax hikes, and we will keep that promise.

“As we speak, Congressional staff are looking at options to rewrite the legislation to meet our pledge. This is what can happen when you have an actual plan and submit it for independent review, which the Democrats who run Washington have refused to do.”

The CBO score appeared to add to Boehner’s troubles as he struggles to corral the House Republican Conference to back his bill on the floor Wednesday.

Using an up-to-date baseline, the CBO estimated that Boehner’s bill would save $850 billion over the next decade, which is less than the immediate $1 trillion debt limit increase that the measure includes. Relative to the January baseline, it would save a bit more: $1.1 trillion. That’s because the up-to-date baseline incorporates cuts already enacted, including the continuing resolution funding the government.

Under the current baseline, the bill would cut the deficit by just $1 billion next year because a $4 billion cut to discretionary spending is partially offset by a $3 billion increase in mandatory spending. The bill actually increases spending upfront for Pell Grants by $4 billion next year, CBO said.

Most of the cuts are backloaded in the second half of the 10-year budget window, the CBO report projects, with just $17 billion in deficit reduction in the first two years combined.

Boehner’s bill, however, also promises much deeper cuts in the future by pegging a future debt limit increase to enactment of a separate $1.8 trillion deficit reduction package by Congress.

But that hasn’t been enough for some conservative Republicans, some of whom have ripped the bill because it would only include relatively small spending cuts upfront, promises of bigger cuts later and no guarantee of enacting a balanced budget amendment to the Constitution.