The White House has "somewhat less leverage" in upcoming budget talks because the "fiscal cliff" deal didn't require a debt-ceiling increase, said former Obama Office of Management and Budget director Peter Orszag.
"But by not insisting that the debt limit be tied to that [cliff] package, it's entirely possible they are going to win the week, but lose the quarter," he said.
He said that President Barack Obama is going to have to negotiate with Republicans on raising the $16.4 trillion borrowing limit, despite claims to the contrary.
To put things in context, the cliff deal only delayed the automatic spending cuts known as the "sequester" by two months. The federal government also faces a shutdown at the end of March if Congress doesn't authorize new funding.
(Read More: Despite Cliff Deal: 'Nothing Really Has Been Fixed')
"If you're negotiating over those things, the debt limit is thrown in. [The president] can say [he's] not negotiating over the debt limit, but there will be negotiations in February and March," Orzag said.
—By CNBC's Matthew J. Belvedere; Follow him on Twitter