Governor Haley Barbour (R-Miss.) talks with reporters during the California Republican Convention in Sacramento, Calif., Saturday, March 19, 2011. (Steve Yeater/AP)

Mississippi Gov. Haley Barbour’s surprise decision on Monday not to run for president set off a scramble inside the Republican Party for pieces of his financial and political network. It also raised questions about the challenges the party may face in trying to unseat President Obama.

So far, the GOP race has been notable for its slow start and the absence of a front-runner. It has been marked by unhappiness among potential voters. The most recent Washington Post-ABC News poll found that barely four in 10 Republicans and Republican-leaning independents said they are satisfied with the current field of candidates — about 20 percentage points lower than at this time four years ago.

Obama, too, is less popular than he was when he was sworn in two years ago. But he comes to the race with the significant advantages of incumbency. As he steams ahead with fundraising and organizing, Republicans are under growing pressure to tamp down concerns about whether they can find a candidate capable of defeating him.

Barbour registered in the single digits in early polls, so his decision will not have a dramatic impact on the contest, at least in terms of voter support. But it will give some candidates an opportunity to nail down some of the volunteers who were committed or leaning toward Barbour as well as money that would have been his.

As a former chairman of the Republican National Committee and the Republican Governors Association, Barbour is the consummate member of the GOP establishment and is widely respected for his political smarts. Other candidates will compete for his endorsement.

His decision not to enter the contest, he said in a statement, grew out of his conclusion that he lacked the necessary fire in the belly. But friends of Barbour, speaking on the condition of anonymity to share insight about his decision, said he had come to the conclusion that Republicans can win only if they are totally focused on serious issues and not distracted by some of the side issues, such as Obama’s birthplace, that have arisen in the early going.

Barbour’s decision may reflect what some Democratic strategists were saying privately: that, for all his political smarts, he would fizzle as a presidential candidate. After all, he carried significant baggage. He was a lobbyist for tobacco companies and other interests, and had stumbled on racial issues over the past six months.

The announcement will put new pressure on some fence-sitters to jump into the race. That pressure will fall most heavily on Indiana Gov. Mitch Daniels, who has been considering a run for more than a year and is planning to decide in May.

Daniels and Barbour are longtime friends and allies — Daniels said recently that if he didn’t run he might well endorse Barbour — and many Republicans assumed that it was unlikely that both would end up in the race.

A close adviser to Daniels said Monday that, “on the margins, it makes it more likely he will run.” But the Indiana governor has been beset by doubts and by what friends say is opposition within his family. He issued a statement praising Barbour as a leader of the party but offered no hint as to his own thinking.

Two candidates — former Massachusetts governor Mitt Romney and former Minnesota governor Tim Pawlenty — will take heart from Barbour’s decision.

Romney, the nominal front-runner, has more space to try to corral establishment support. But there are doubts about his candidacy in some quarters because of his support for a health-care plan in his state that strongly resembles Obama’s health-care law, and because of continuing questions about his authenticity.

Pawlenty, who has feet in the establishment and the conservative grass-roots camps of the party, will look to expand his appeal among both and will quickly reach out to Barbour’s fundraisers.

Some possible candidates could be affected by Barbour’s decision. Former Arkansas governor Mike Huckabee, who is at the top of many national polls of Republicans but who has been putting off a decision until later in the summer, could see the South opening up even more to him with Barbour on the sidelines. Former House speaker Newt Gingrich (Ga.) may go hunting for some of Barbour’s financial supporters.

Meanwhile, Jon Huntsman Jr., who is finishing a stint as U.S. ambassador to China and is weighing a campaign, could get a closer look from establishment Republicans and grass-roots activists as a fresh face.

The potential field includes many others who are competing for other parts of the party’s coalition and for public attention. That group includes businessman Donald Trump, who has been raising questions about Obama’s birthplace; Rep. Michele Bachmann (R-Minn.), a favorite of tea party activists; and former senator Rick Santorum (Pa.), who has solid roots among social and religious conservatives.

Rep. Ron Paul (R-Tex.), who has a small but passionate following of his own, appears ready to compete again on his libertarian agenda. Former Alaska governor Sarah Palin might yet make waves if she shows interest in running in the coming weeks.

The field also includes two long shots, businessman Herman Cain and former Louisiana governor Buddy Roemer, which means a clogged stage and potential sideshows at the early debates for a party attempting to prove that it is ready to take over the White House again.