WARRENVILLE, S.C. — An upbeat Newt Gingrich closed out a town hall meeting here Wednesday with a prediction that Mitt Romney’s campaign will come after him hard between now and Saturday.

“I think they will be unendingly dirty and dishonest for the next four days, because they’re desperate,” Gingrich told an overflow crowd at a barbecue restaurant. “They thought they could buy this. They’re discovering they can’t buy this. I think they have internal polls that show him losing. I think they will be anything at any level, and I need your help.”

Gingrich has seized on Romney’s missteps on the issue of releasing his tax returns and, according to spokesman R.C. Hammond, plans to add to the pressure on his rival by releasing his 2010 tax returns on Thursday. That will tee up the tax issue in advance of Thursday night’s debate in Charleston.

Gingrich’s campaign sought to counter the latest efforts by Romney to discredit him as unreliable, issuing a list of names of current and former House members who praised him as an effective speaker after he led the Republicans to power in the House in the 1994 elections.