He said this would prevent the government from reaching the borrowing limit for about another two months.
This $16.4tn is the amount the government is allowed to borrow to finance its operations.
Silent corridors
Mr Obama is expected meet Republican leaders again to try to negotiate a solution, although no new date has been announced.
Failure to do so could damage the US and global markets, and threatens to send the US economy into recession.
The two sides remain far apart on the fiscal cliffs $600bn in tax rises and spending cuts, but analysts say a short-term deal may be agreed that will postpone the cuts until spring.
On Wednesday, the Republican House of Representatives Speaker John Boehner called on the Democrat-led Senate to come up with legislation on how it would avoid the cliff, and pass it to the House for consideration.
However, a senior administration official said it was up to Republican leaders not to stand in the way of an agreement.
Despite this, there is little sense of urgency in the capital - the corridors of Congress are silent, the BBCs Zoe Conway in Washington reports.
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