One week before Republican voters begin selecting a presidential nominee, the race in Iowa is as muddled as any in recent times as six candidates set off on a sprint to win a contest that leading strategists here say is up for grabs.

Former House speaker Newt Gingrich, who only a few weeks ago had a clear lead, appears to have lost significant ground under an onslaught of negative advertisements. One beneficiary may be former Massachusetts governor Mitt Romney, who had been making only sporadic appearances in Iowa but this week begins a concerted late push, with operatives in the state suggesting he might actually win.

Rep. Ron Paul (Tex.), whose campaign organization remains strong, has run into controversies over racially charged writings, while three second-tier candidates are trying to seize momentum. One of them, former senator Rick Santorum (Pa.), got the backing of two leading conservatives last week and is seen by strategists as beginning to make a move, although the question is how significant it might be.

“I’ve never seen it this fluid, this late in the process, with this many candidates,” Iowa GOP Chairman Matt Strawn said. “In the past, maybe it’s been down to a binary choice of a couple of candidates, but the fact that half of Iowans are telling pollsters they could change their minds is unprecedented.”

Santorum was the only candidate in the state Monday. He went bird hunting with Iowa conservatives, including Rep. Steve King, whose endorsement most candidates are aggressively seeking. King said after the hunt with Santorum that he remains undecided.

“Our campaign is clearly the one that is rising right now and has the momentum,” Santorum, who was wearing bright-orange hunting gear said. “No votes have been cast, and I feel very, very good that all the work that we’ve done, all the groundwork we’re doing, the foundation we’ve laid is coming and working just perfectly.”

The other candidates are set to return Tuesday for their final pushes after a weekend break for the Christmas holiday. In the meantime, Romney and Texas Gov. Rick Perry launched television advertisements Monday that seemed designed to appeal to tea party activists. Romney focused on cutting government spending while Perry pumped his proposal to turn Congress into a part-time institution.

Gingrich, who is trying to regain some of the enthusiasm that lifted his candidacy early in the month, began to draw fresh contrasts with Romney over his economic policy and avowed conservatism. In a statement, the Gingrich campaign asked: “Can we trust a Massachusetts Moderate to enact a conservative agenda?”

Gingrich last week acknowledged that the negative ads — aired by a political action committee financed by Romney allies as well as Paul’s and Perry’s campaigns — had hurt him here and that he would have to fight back more aggressively. Gingrich plans to contrast his tax proposals with Romney’s, which his campaign will describe as “timid” and “moderate,” through conservative surrogates as well as the candidate himself on a 44-stop bus tour, according to a senior campaign official.

But some Republican operatives question whether it is too late for Gingrich to regain his standing.

“These negative ads that are running against him are effective,” Iowa strategist Craig Robinson said. “There’s not going to be any singular moment where he can regain the footing. Nothing will allow him to pull the break in these polls.”

Romney will touch down in the Hawkeye State on Tuesday afternoon to deliver a speech in Davenport. He will then embark on a three-day bus tour through communities where he performed well in the 2008 caucuses. Romney also will employ a series of surrogates, including New Jersey Gov. Chris Christie and Sen. John Thune (S.D.), to help blanket the state with his message.

Perry and Rep. Michele Bachmann (Minn.), who promised to hit all 99 counties in the final weeks, will lead their own bus tours Tuesday.

All other candidates concede that Paul has a strong organization but contend that there may be a ceiling to his support. The controversy over newsletters produced in the early 1990s, in between his stints as a member of Congress, threatens to disrupt his message. Written in the early 1990s, the newsletters, circulated in libertarian circles, included highly insensitive writings about racial issues and black leaders and activists.

Paul has disavowed the writings and said he never read them until years later. But he is likely to face questions when he returns here.

The contest has lacked the intensity of past Iowa campaigns, with the leading candidates making vastly fewer visits. But this week marks a newly frenetic pace of retail campaigning, with Republican voters giving the candidates a final look before heading into the Jan. 3 precinct caucuses.

“All those undecided voters we’ve been talking about for months will firm up,” said Iowa GOP operative Tim Albrecht. “All the candidates are doing the right things, and that is they’re hopping on a bus and making the final pitch to Iowans. There’s no better way to secure support for the caucuses than to look an Iowan in the eye and ask for it.”

GOP leaders in some of the state’s biggest Republican strongholds described an unusual state of uncertainty, with no clear favorite heading into the caucuses. They said anecdotal evidence suggests that after visiting all 99 counties, many of them multiple times, Santorum’s hard work may finally be paying off with a late surge. But he has yet to make a sizable leap in public polling.

“He’s working very hard to drive his turnout up, and he’s made a very favorable impression on people,” said Bob Anderson, chairman of the Johnson County Republican Party, who noted an uptick in Romney’s support as well.

The Tuesday evening caucuses, held in 1,774 precincts, will be in part a battle of turnout. GOP officials estimated that turnout could be as high or higher than in 2008, when a record 119,118 Iowa Republicans participated.

Former Arkansas governor Mike Huckabee won the 2008 caucuses with 34 percent of the vote, but Iowa strategists believe that this time, with so many candidates bunched near the top, a candidate could win with a smaller plurality. The lowest winning percentage was Robert J. Dole’s 26 percent in 1996.

“We’re expecting a good turnout,” said Brian Rosener, chairman of the Woodbury County Republican Party. He added that his office has received “a lot of calls from people who haven’t done it before asking what do I do, where do I go, how does it work, and even some Democrats calling in to say they’re switching parties.”