Early in October, Newt Gingrich was completing a busy three-day swing through South Carolina. He had met with Tea Party members and others, and despite bad poll numbers — fallout from a disastrous summer after his top aides quit en masse — he was beginning to sense a change in his fortunes.

"I’ve got a crazy idea," Gingrich said to Adam Waldeck, a 26-year-old aide who was driving him in a rental car to the Charleston airport. "What do you think of moving down here full time? I think we can win South Carolina."

It did seem crazy. Gingrich was heavily in debt, had no campaign infrastructure and had been left for dead as the race for the Republican nomination for president moved on without him.

But his instincts were right. Things were changing, and soon they would change dramatically. His debate performances, which showcased his range of knowledge, combativeness against President Barack Obama and the media, and mastery at generating free publicity, earned him another look from voters.

More people were showing up to see him. Money started trickling in, and he was able to make strategic moves, like staking a claim in South Carolina. Amid an anti-Washington mood, he reveled in the bare-bones nature of his campaign, denouncing the influence of consultants he could no longer afford; his wife, Callista, whom many of his aides had blamed for the problems that led to his campaign’s summer meltdown, took on a more active behind-the-scenes role, installing a friend as campaign manager, redesigning the campaign logo and coaching Gingrich on his stage performance.

And one by one, his rivals as the alternative to Mitt Romney collapsed.

By fall, Gingrich was positioned to make a remarkable recovery. He lifted himself from a low of about 2 percentage points in the polls in mid-June to the lead in many national and state polls today. With just 16 days until Republican voters begin choosing a nominee at the Iowa caucuses on Jan. 3, he is favored in three of the four early voting states — the exception is New Hampshire, Romney’s adopted home state — giving him a shot at establishing a commanding position in the race’s opening stage.

Gingrich has hardly dispatched all of his problems. He still has vociferous opponents within the Republican establishment. While he is quick-witted and tough, they say, he is also incendiary and undisciplined and carries too much personal baggage.

As the perceived front-runner, he is drawing a barrage of attacks from his rivals. His strategy appears to be made up almost hour by hour — he initially planned to spend this weekend at home, before adding a Sunday-morning television appearance and conference calls with reporters and supporters — and he is far behind Romney in fund-raising and get-out-the-vote efforts.

Gingrich’s supporters acknowledge that his comeback tale entailed a huge amount of luck.

"The main thing the campaign did over the summer months was keep him alive," said Robert S. Walker, a former Republican congressman from Pennsylvania and now an adviser to Gingrich. "We were working with very limited resources and a small staff."

But if Gingrich can sustain his resurgence, it will be one of the most striking turnarounds in American politics. After about 15 of his aides and advisers quit June 9, the campaign was a shambles. The advisers blamed Callista Gingrich for diverting him from campaign activities. He was still a late-night punch line, after Politico reported that he had a $500,000 line of credit at Tiffany’s.

Gingrich, 68, has said June and July were the worst months in his political career, which is saying a lot, considering his own party dethroned him as the speaker of the House in 1998. After the exodus in June, his remaining staff members thought he was going to throw in the towel but were surprised when he told them that he was staying in, partly at the urging of Callista Gingrich.

"His wife had said to him, ‘Don’t you dare,’ " said R.C. Hammond, his press secretary. She convinced him that he could turn the debates to his advantage, and a friend of hers from college, Michael Krull, came on board as campaign manager.

The campaign was in debt and operating on a shoestring. But the long series of debates kept Gingrich afloat, putting him on equal footing with his rivals in televised events that got strong ratings and became the central campaign forum for the candidates.

Hammond cited the Aug. 11 debate in Ames, Iowa, as a turning point. "He walked into that debate DOA," Hammond said, "and when he walked out he had regained his pulse."