As Speaker John Boehner was rewriting his deficit reduction proposal Tuesday night because the Congressional Budget Office said its cuts were smaller than advertised, the Ohio Republican got some support from an unusual source: the White House.

Jacob Lew, the director of the Office of Management and Budget, argued in a blog post that the spending cuts in Boehner’s measure should be tallied as $1.2 trillion over the next decade, not the $850 billion that the CBO cited. Lew said that’s because all of the deficit reduction discussions so far have been working off of the CBO’s January baseline, not the most recent version, which reflects cuts already made in the continuing resolution funding the government and other laws.

Using the up-to-date baseline would be “confusing,” Lew wrote.

“Don’t get me wrong: there is a lot in Speaker Boehner’s plan that we do not like and actively oppose. But, as this debate continues and intensifies in the coming days, it’s important that we compare apples to apples, and make sure that we are all understanding the facts,” he wrote.

The White House appears to be worried that using the newer baseline would make all of the packages of cuts on the table look significantly smaller. It could also raise the bar for cutting in the short term as lawmakers and the White House struggle to strike a deal on a deficit reduction package that would raise the nation’s debt ceiling.

Boehner’s proposal, according to the CBO, cuts the deficit next year by just $1 billion and $16 billion in fiscal 2013, much less than many conservatives want.