The President could ease the restrictions with a stroke of his pen, but he must give Congress six months to review the decision.
He said the proposal also could be fashioned to give Congress more oversight.
The vote gives Congress and the President one of their few legislative feats.
What powers does the Constitution give Congress that affect the other two branches?
But they made little secret of their position that the current caps have little value given the way Congress has maneuvered around them.
The Senators said the new proposal would probably give Congress an additional year, until 1992, to reduce the deficit to zero.
When viewed together with the broad powers the Court has given Congress in the 20th century, the decision seems fundamentally flawed.
She is giving Congress 90 days to put into effect a very general decree on breaking up baronial estates.
The act gives Congress 60 days to reject final regulations issued by federal agencies.
The President said the bill gave Congress "a chance to be tough and smart."