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.
In recent days, Republicans, who control the House of Representatives, and Democrats, who control the Senate, have rejected plans drawn up by the rival party in an unprecedented political battle.
Mr Obama opposed the Republican plan because it would only have raised the debt limit by enough to last until mid-2012, meaning Washington would have had to readdress the issue during next year's presidential campaign.
He said the plan announced on Sunday, if approved, would avoid such a scenario.
Watch Obama's speech here: