NEW YORK — Even with the deal to raise the federal government’s debt ceiling, the U.S. could still lose its coveted AAA debt rating sometime in the next six months, largely because the agreement does not cut enough spending.

The three main ratings agencies declined to comment Monday on the prospect of future downgrades. But the agencies, along with economists and analysts, have signaled that doubts about the nation’s debt will persist.

Moody’s Investors Services has said it will probably rate the U.S. debt as AAA for now but with a negative outlook — a rating that indicates a possible downgrade yet to come.

Fitch Ratings has indicated the deficit must be reduced to a “more sustainable level” for the U.S. to maintain its AAA rating. And Standard & Poor’s has said any deal to raise the debt ceiling must cut at least $4 trillion from future budget deficits or the rating will probably be lowered to AA.

The deal crafted by Obama and congressional leaders cuts only about half that amount, which led at least one expert to suggest that S&P could still downgrade the rating as early as next month.

“The details [of the deal] don’t look as pretty as the headlines,” said Guy LeBas, chief fixed income strategist at Janney Montgomery Scott.

Ratings agencies probably won’t look favorably on the fact that most of the spending cuts in the current plan won’t be made until after 2013, LeBas said.

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