Lawmakers said the goal was to present a final proposal to a joint House-Senate negotiating committee on Monday.
As war loomed in 1941 Congress approved his proposal for a joint House-Senate committee to look into ways of eliminating nonessential expenditures.
Others involved in the House-Senate negotiating committee sounded less optimistic.
The House-Senate committee addressing the issue remains deadlocked, as the White House acknowledged this week.
The joint House-Senate committee conducting the Sept. 11 investigation has already been briefed on the F.B.I. memorandum, officials said.
A final budget is currently being hammered out by a joint House-Senate committee.
The tax compromise, reached by a joint House-Senate committee over the weekend, included maintaining a temporary increase in the fuel tax, now 15 cents a gallon.
By sabotaging a crime bill agreed to by a joint House-Senate committee, Senate Republicans have left themselves facing the election empty-handed.
If sufficient progress is made, they said, a final proposal could be presented to a House-Senate negotiating committee as early as Thursday.
Les Aspin, a Democratic member of the House-Senate committee, said, "There's got to be another source of funding."