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“I will not sign a plan that adds one dime to our deficits, either now or in the future. Period,” he said.

So far, however, all current proposals fall short of the mark.

The Congressional Budget Office found in July that the House bill will increase the deficit by $239 billion over the 2010-2019 period. And on Wednesday morning, hours before Mr. Obama’s speech, a new study showed that the nation’s budget imbalance would skyrocket after 2020 under the same piece of legislation.

The House bill would increase the budget deficit by $1 trillion between 2020 to 2029, up from a $39 billion increase from 2010 through 2019, said a Peterson Foundation study conducted by the nonpartisan Lewin Group. The overall cost of the bill would be roughly $3 trillion from 2010 to 2029, the study said, and is currently only offset by savings and new revenue of about $2 trillion.

Mr. Obama promised “a provision in this plan that requires us to come forward with more spending cuts if the savings we promised don’t materialize.”