On his first trip to Iowa this spring, Mitt Romney was asked a question that has been hanging over his campaign ever since: Could he win the Iowa caucuses after exhausting his time and money here four years ago for a debilitating second-place finish?

Romney never answered the question. A fire alarm went off. Somewhere upstairs, a bag of popcorn was burning inside a microwave oven. Everyone evacuated the building; Romney climbed into an SUV and off he went.

Now, with a week to go before voters provide the answer that Romney didn’t, the former Massachusetts governor appears to have about the same level of support as four years ago — only this time that could be enough to win Tuesday’s contest and put him on a path to quickly lock up the Republican presidential nomination.

“They’re trying to get new supporters,” said Brent Siegrist, a former Iowa House speaker who endorsed Romney four years ago and has again this time. “But obviously if they could turn out voters like they did last time, given the split on the Christian conservative side, Romney could end up doing pretty well.”

Returning to Iowa on Tuesday night to deliver a speech kicking off his final burst of campaigning, Romney looked out across the opulent ballroom of a downtown hotel here and wondered whether he had attracted some new backing. “The hallways are full, the stairways are full — this is just amazing,” he exclaimed. “I don’t know how you got here, but I appreciate it.”

The visit was only the eighth of the year for Romney. He is to embark on a statewide bus tour Wednesday and is dispatching a band of surrogates, including New Jersey Gov. Chris Christie, to deliver his message across this state.

For months, Romney, the national front-runner, ran a stealth Iowa campaign designed to manage expectations — shoring up enough support to avoid a disastrous result, but not doing so much that he would have been expected to win. But under the radar, his staff and supporters here have pursued a strategy to squeeze every vote out of a state that is seen as inhospitable to Romney.

“Romney’s advantage this time is that he is the only candidate [other than Rep. Ron Paul] who has worked a caucus campaign previously, so he knows what to expect and knows how to effectively manage expectations,” said Iowa strategist Tim Albrecht, who worked on Romney’s 2008 campaign but now works for Gov. Terry Branstad, who has not endorsed a candidate.

Last time, Romney paid an army of field staff and political endorsers here to build a network of supporters. This time, he is relying mostly on volunteers and a far slimmer paid staff. Instead of blanketing the state as Team Romney did in 2008, they are focusing their efforts on the precincts where they did well four years ago.

Romney has also been sure to maintain some presence. One of his few field staffers, Phil Valenziano, drove to Republican events across the state this summer, manning a folding table with campaign fliers and bumper stickers and recruiting new supporters.

“We didn’t want to leave the impression we weren’t putting in the effort here,” said David Kochel, Romney’s Iowa strategist.

The Romney campaign also has a database of his 2008 supporters and has checked in with them throughout the year, signing up hundreds as volunteer precinct captains. The campaign knows who to dial for town hall meetings by conference call, such as the one Romney held Monday, or for more intimate telephone sessions with business people.

“We started with a blank piece of paper four years ago,” said state Rep. Renee Schulte, who ran Romney’s efforts in populous Linn County last time and is a state campaign co-chair now. “We, of course, have kept all that data. So now this year, I still have the list and I still know all the people.”

Siegrist said that in a 24-hour span this week, he received three robo-calls from Romney’s campaign — one with precinct-specific instructions for how to participate in Tuesday’s caucuses and two for a pair of teleconference town hall meetings, one with Romney and one with Arizona sheriff Paul Babeu, a Romney surrogate.

Not only have Romney’s visits to the state been few and far between, they have also been in carefully selected venues in carefully selected towns before carefully selected audiences at carefully selected moments.

Romney interacts with voters mostly at town hall meetings or during economic roundtables in factories and other businesses — events choreographed to keep voters’ questions focused on the economic matters in his wheelhouse rather than the social issues that dogged him in 2008.

Romney met with farmers and ranchers at a bank in Treynor, with Republican activists at a picnic in Cedar Rapids, with business folks at a manufacturer in Pella and the Chamber of Commerce in Council Bluffs. But he has chosen to skip all of Iowa’s “cattle call” forums that have attracted the other candidates.

On Tuesday, Romney gave a 15-minute speech with what sounded like a general election message. He focused solely on President Obama and his economic record, accusing Obama of not living up to the promises he made when he campaigned in Davenport four years earlier, nearly to the day.

“He closed with these words: ‘This is our moment, this is our time,’ ” Romney said. “Well, Mr. President, you have had your moment. We have seen the results. And now, Mr. President, it is our time.”

This strategy may bear fruit for Romney, but what may seem like a brilliant strategy if he wins on Tuesday is really just a matter of due diligence. “There’s no magic genius to what we’re doing,” Kochel said. “We’re doing the blocking and tackling and recruiting of volunteers that every campaign does.”

If Romney wins, strategists here say, it will probably be by a small plurality, with a percentage of the vote similar to the 25 percent he won in 2008. Asked about his chances in Iowa, Romney told reporters on Tuesday: “I don’t have any predictions. No expectations are set. We’re hoping to do well everywhere.”

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Staff writer Sandhya Somashekhar in New Hampshire contributed to this report.