The announcement Sunday by Gov. Mitch Daniels of Indiana that he would not run for the Republican presidential nomination ended one major chapter of uncertainty in the race but ignited new debate over whether the current field contains a candidate capable of beating President Obama next year.
Saying that his family did not want to go through a campaign, Mr. Daniels became the third high-profile Republican in eight days to choose not to compete for the chance to challenge Mr. Obama. The contest is now increasingly focused on three former governors — Mitt Romney of Massachusetts, Tim Pawlenty of Minnesota and, to a lesser extent, Jon M. Huntsman Jr. of Utah.
Mr. Daniels's decision was one of the most anticipated events of the early campaign season, and he reached it just days after former Gov. Mike Huckabee of Arkansas and the developer Donald J. Trump said they would opt out of a race. Mr. Daniels faced considerable pressure from a wide spectrum of Republicans to enter the race, and he had signaled that he would focus on addressing the nation's fiscal issues.
But after weeks of deliberating in public and making clear that his wife and four daughters had deep reservations — caused in part by the knowledge that they would be exposed to intensive scrutiny over a period in the 1990s when Mr. Daniels and his wife, Cheri, divorced and then remarried — he said he was unsuccessful in swaying his family.
In a statement on Sunday he said, "Our family constitution gives a veto to the women's caucus, and there is no override provision."
His decision left the party split between those who said the current crop of candidates would grow in stature and appeal as the campaign progresses and those who continued to hope for new entrants capable of mobilizing conservative energy.
"Everybody is waiting for Superman, and soon they will learn that Superman is already in the race," said Fred V. Malek, a longtime Republican fund-raiser and adviser. "I believe the field is now complete and is now strong, with three former governors who have records of cutting costs and balancing budgets."
Other establishment Republicans said Mr. Daniels's announcement would direct the focus toward candidates who are certain to run and limit calls for wish-list candidates to enter the race, which undermine the field of real potential contenders.
In particular, Mr. Pawlenty and Mr. Huntsman now have clearer opportunities to establish themselves as the main alternatives to Mr. Romney, who was a candidate in 2008 and has built a formidable fund-raising network this time around.
"The field is largely now settled, and Republican activists and donors will begin increasingly choosing between those who are declared," said Ed Gillespie, a former chairman of the Republican National Committee and an adviser to President George W. Bush. "The process will accelerate now."
But with at least eight months remaining before the first votes are cast, some influential party voices said that it was not too late for other candidates. Gov. Chris Christie of New Jersey, Representative Paul D. Ryan of Wisconsin and former Gov. Jeb Bush of Florida were among those mentioned anew on the Sunday television news shows, but none showed any indication that they would join the race.
"I've been very clear about this," Mr. Ryan said on "Meet the Press" on NBC. "I'm not running for president."
Mr. Pawlenty, who is little known among most voters, is set to formally declare his candidacy on Monday in Iowa. But he got a jump on his own announcement on Sunday night, releasing a video on YouTube saying, "I'm Tim Pawlenty, and I'm running for president of the United States." Mr. Huntsman, who returned only weeks ago from Beijing where he was Mr. Obama's ambassador to China, is finishing a five-day trip to New Hampshire.
Mr. Romney faces opposition from many conservatives because the health care law he signed in Massachusetts resembles the national measure backed by Mr. Obama, but he has a robust campaign operation under way. Other candidates, including Newt Gingrich, the former House speaker, are battling self-inflicted problems and other challenges to becoming credible challengers.
"The chattering class in Washington will run around for a while with their hands up in the air, but I think the field is pretty much settled," said Mr. Huntsman's senior strategist, John Weaver.
Sarah Palin, a former governor of Alaska, has yet to declare her intentions and is seen as a rare contender who could jump in at the 11th hour. Representative Michele Bachmann of Minnesota, who has appeal among social conservatives in states like Iowa, is also considering a bid.
In a statement, Mr. Pawlenty sought to take up Mr. Daniels's mantle of fiscal restraint, saying, "Mitch and I agree that America's out-of-control national debt is a threat to our nation’s future." Mr. Huntsman hailed Mr. Daniels for "the steadfast manner in which he's shined a light on the crippling debt that we will leave behind for future generations."
Ms. Palin's candidacy could remain the biggest question mark of the campaign. She made appearances on the programs of Sean Hannity and Greta Van Susteren of Fox News Channel over the last week, telling Ms. Van Susteren on Thursday, "I have that fire in my belly" for a presidential run, but saying she had other considerations, including the effect on her children.
Mr. Daniels's decision was a disappointment to supporters, including some officials he had served with in the administration of President George W. Bush, where he was budget director, and to some Bush donors, who had signaled they would rally around his candidacy.
"In the end, I was able to resolve every competing consideration but one," Mr. Daniels wrote in an overnight message to supporters. "The interests and wishes of my family is the most important consideration of all."
The Daniels family saw a glimpse of the spotlight when Cheri Daniels agreed to make a rare public speech at the spring dinner of the Indiana Republican Party. Her appearance touched off stories about the couple's divorce in 1993 and Mrs. Daniels's decision to move briefly to California with another man, whom she married in 1995. Two years later, she remarried Mr. Daniels.
In Indiana, Mr. Daniels has been portrayed as the father who raised his four daughters when Mrs. Daniels moved away. A review of the divorce file in Boone County Court showed that Mrs. Daniels tried to take her daughters, 7 to 13 at the time, to California, but that Mr. Daniels blocked her effort with an emergency appeal to the court.
He also tried to block her effort to buy a house, court records show, but a judge overruled his request. She moved back to Indianapolis and had joint custody of the children until the couple remarried.
In a statement on Sunday to The Indianapolis Star, Mr. Daniels sought to clarify that episode, saying they had raised the children together. "The notion that Cheri ever did or would abandon her girls or parental duty is the reverse of the truth and absurd to anyone who knows her," he said.