Indiana Gov. Mitch Daniels’s decision not to run for president in 2012, while deflating the hopes of many in the Republican establishment, has helped solidify what has been a fluid GOP field and brings more clarity to the challenges ahead for each of the leading contenders.

Daniels, who had been deliberating for more than a year, made his announcement around midnight Saturday. He joined a growing list of potential candidates who looked at the race and decided to take a pass.

GOP strategists say that the removal of Daniels as a factor has made it even more obvious that the contest is becoming one between presumed front-runner Mitt Romney and a pack of underdogs hoping to emerge as the alternative to the former Massachusetts governor.

There are still a handful of possible candidates — among them, former Alaska governor Sarah Palin and Rep. Michele Bachmann of Minnesota — who have not yet announced their intentions.

And the dismay that some influential Republicans are feeling over Daniels’s refusal to run may well spark a renewal of their efforts to coax such conservative stars as ex-Florida governor Jeb Bush and current New Jersey Gov. Chris Christie into the race.

On Sunday afternoon, Bush was getting entreaties by e-mail, one associate reported. On Sunday night, he released a statement saying: “While I am flattered by everyone’s encouragement, my decision has not changed. I will not be a candidate for president in 2012.”

Those who are close to the Indiana governor say that he had wanted to run, if only to make sure that the issues of economic growth and fiscal discipline with which he has been so closely associated would get their due. But ultimately, he yielded to the opposition of his wife and four daughters.

“Simply put, I find myself caught between two duties. I love my country; I love my family more,” Daniels wrote in an e-mail to supporters.

Daniels and his small team had actually been well on their way to a candidacy, according to Mark Lub­bers, a longtime Daniels adviser. Legal documents to form some kind of presidential committee had been drafted. Daniels’s advisers had held conversations with people interested in helping to staff the upper ranks of the campaign. Potential supporters, including members of Congress and other elected officials, were in the queue in anticipation.

Some of this work was done without the explicit approval or direction of Daniels, as his advisers waited for the governor and his family to come to a decision. He hoped his wife, Cheri, and their daughters would relent and give him the okay. In the end, they did not.

On Friday, Daniels asked that a conference call be set up for Saturday with a handful of advisers who had first urged him to consider running more than a year ago. Daniels read advisers the statement he would later give to the Indianapolis Star as well as a message e-mailed to supporters by Indiana Republican Party Chairman Eric Holcomb.

“His voice broke only one place when he read it to us,” Lubbers said. That was where Daniels expressed his sorrow that he had disappointed his allies, and added: “If I have disappointed you, I will always be sorry. If you feel that this was a non-courageous or unpatriotic decision, I understand and will not attempt to persuade you otherwise.”

Lubbers said reaction to Daniels’s decision has been one of sadness by many who were urging him to run, especially among those who saw in the governor someone who “was on to something and was tapping into it in a way that would have made a difference. . . . They have this sense that the moment may be lost.”

Not surprisingly, those who have already signed up for the leading contenders said Daniels’s absence would work to their candidate’s benefit. For once, they may all be right.

“Any first-tier candidate or candidate who aspires to be in that first tier is a beneficiary,” said Republican strategist Brian Jones, who worked for GOP nominee John McCain in 2008.

For starters, the resolution of one of the biggest questions about the race could draw in donors and activists who have been sitting on the sidelines. It also could help shift the public’s attention from the candidates’ backstage deliberations to their messages.

“The field is set,” senior Romney adviser Stuart Stevens said. “The economy is the dominant issue. So now we start to focus on who is the best on [the] economy.”

But for all of Romney’s assets, including fundraising firepower demonstrated earlier this month by a phone bank that raised more than $10 million in a single day, his uneven performance in his unsuccessful 2008 bid has left many Republicans doubtful that he has the political skills it will take to beat President Obama.

That is why the search for an alternative has, by some measures, made this the most wide-open nominating contest in half a century or more.

With Daniels’s decision, “it opens up some more airspace,” said Phil Musser, a senior adviser to former Minnesota governor Tim Pawlenty, who declared in a video Sunday night that he is running for president and will make his formal announcement Monday. The first caucus in Iowa is crucial to Pawlenty’s viability, and Daniels could have presented formidable competition for the regional loyalties of Midwesterners.

Another camp buoyed by Daniels’s announcement was that of the freshest face in the field, former Utah governor Jon Huntsman Jr., a potential candidate who will wrap up a five-day swing through New Hampshire on Monday. Like Pawlenty, he is trying to sell himself as someone who has crossover appeal outside the GOP base.

“For all the talk that the field is still unsettled, it really isn’t,” said John Weaver, a former McCain strategist who is the top adviser to Huntsman. “I think it leaves only one credible fiscal conservative who has the ability to win both the primary and the general election.”

Daniels’s decision came at the end of a week that saw enormous upheaval in the race.

Former Arkansas governor Mike Huckabee, who won the Iowa caucuses in 2008, announced that he would not be a candidate, as did reality-TV star and real estate developer Donald Trump. Last month, Mississippi Gov. Haley Barbour announced that he would not run, after making several swings through the early primary states.

Meanwhile, Newt Gingrich’s candidacy got off to a rocky start. The former House speaker spent most of his first week as an official candidate trying to clean up the damage from comments he made on NBC’s “Meet the Press.” Among the most inflammatory was his suggestion that a GOP effort to revamp the Medicare program — which nearly every House Republican is on record as voting for — amounts to “right-wing social engineering.”

On Sunday, Gingrich attempted a do-over on CBS’s “Face the Nation,” telling host Bob Schieffer, “I probably used unfortunate language about social engineering.”

For all the Republican hand-wringing over the state of the race, there is one place where the strength of the potential field is not being discounted: the Obama White House.

Strategists there note the country is so divided that any credible contender is likely to emerge from the nominating contest with a strong, energized base of support and adequate financial resources.

Said one adviser to the Obama reelection campaign, who spoke on the condition of anonymity: “Through the process of winning that nomination, they will achieve stature, and by the reality of having won that nomination, they will be competitive with the president at fundraising.”

Added another: “Unless it’s Palin or Gingrich, we expect a very close race no matter who emerges.”