According to a report by the BBC, Obama said the deal would cut $1 trillion of spending over the next 10 years, and a committee would be set up to report by November a proposal to further reduce the deficit.
But Congress still has to approve the deal, and no votes are expected until Monday at the earliest.
The parties face a Tuesday deadline to raise the $14.3 trillion debt limit.
The US president said it was not the deal he would have preferred, but noted that the compromise plan would make a "serious downpayment" on the US deficit.
Democrats and Republicans in Washington have been deadlocked over finding a plan on how to cut spending and raise the debt limit as the Tuesday deadline approaches.
According to Mr Boehner, those savings would amount to at least $1.5 trillion, bringing the total spending cuts under the plan to about $2.5 trillion.
That would be higher than the proposed rise in the debt limit, which an administration official said would amount to $2.1 trillion.