Mr Gingrich has vowed to stay in the contest following Tuesday's exit of Republican rival Rick Santorum.
But front-runner Mitt Romney is expected to wrap up the race by June.
"It is now a 2 person race," the former House Speaker tweeted, calling himself "the last conservative standing".
Mr Gingrich's campaign, which cut a third of its staff in March, told ABC News on Tuesday it was $4.5m in debt.
It was reported last month that the Gingrich campaign's latest fundraising tactic was to charge people $50 to have their photo taken with the candidate.