Detroit (CNN) -- A relieved Mitt Romney hailed his big night Tuesday after winning crucial primaries in Arizona and his childhood home of Michigan to revitalize his campaign for the Republican presidential nomination.
Romney needed to win both states, but especially Michigan -- where he grew up when his father was governor -- to assert his ability to overcome the conservative challenge from former Pennsylvania Sen. Rick Santorum.
In a speech to supporters after CNN projected his Michigan victory, Romney acknowledged the outcome was closer than he would have liked.
"A week ago, it was just a week ago, the pundits and the pollsters, they were ready to count us out," he said of surveys that showed Santorum leading in Michigan. " ... We didn't win by a lot, but we won by enough and that's all that counts.
A Santorum victory in Michigan would have been a major upset, and raised more questions about how strong a candidate Romney is within his own party.
In Michigan, Romney was ahead with 41% to 38% for Santorum, 12% for Texas Rep. Ron Paul and 7% for Newt Gingrich, with 86% of unofficial returns counted.
The state's 30 delegates will be allocated on a proportional basis, and Romney and Santorum each won three so far, according to the returns. However, it was unclear who would win the most Michigian delegates, which are based on congressional districts.
Romney's victory in Arizona was expected and more thorough. He had 48% to 26% for Santorum, 16% for Gingrich and 8% for Paul with 75 of the unofficial returns counted. The result gave Romney all of the state's 29 delegates in the winner-takes-all primary. Trailing well back were Gingrich and Paul.
Santorum portrayed his Michigan defeat after leading in the polls as a better-than-expected performance on Romney's home turf.
"This was going to be Romney's night. The question was how big. And it wasn't very big," Santorum said. The outcome showed it was a "two-person race right now" between himself and Romney, he added.
Speaking to supporters, he played up his showing as a sign of better things to come.
"A month ago they didn't know who we are, but they do now," Santorum said, calling it "an absolutely great night."
"The people of Michigan looked into the hearts of the candidates, and all I have to say is 'I love you back,' " he added.
Santorum and Gingrich are vying for the support of conservatives to try to overcome Romney's advantage in spending and organization.
The results Tuesday showed that combining the support for Santorum and the former House speaker would equal or exceed Romney's support, a point certain to heighten the competition in coming weeks as the campaign heads toward Super Tuesday on March 6 and beyond.
Early exit polls in Michigan showed frustration with the Republican field, according to those who responded to questioners.
Less than half of voters in the Republican primary said they strongly favored their own candidate, while 52% had reservations or disliked the other candidate more, according to the exit poll data.
Santorum launched automated phone calls Monday asking Michigan Democrats to vote for him in the open primary "to send a loud message to Massachusetts' Mitt Romney." In Michigan's primary, all voters can participate regardless of party affiliation.
Liberal bloggers also have been asking Democrats and independents to vote for Santorum as a way of damaging Romney's chances of winning the nomination.
Speaking to reporters in Livonia, Michigan, on Tuesday morning -- his first news conference in nearly three weeks -- Romney called the tactics by Santorum and Democrats "a real effort to kidnap our primary process."
He called on Republicans to turn out "and say no to the dirty tricks of a desperate campaign."
Santorum defended the calls to Democrats at a campaign stop Tuesday in Kentwood, saying Romney used the same tactics earlier when he encouraged New Hampshire voters to cross over to support him.
A majority of voters in New Hampshire, which Romney won last month, were independents or Democrats, Santorum noted.
"And when he goes out and recruits folks who aren't Republicans, that's all right," said Santorum, who later said of Romney: "That's what bullies do -- when you hit 'em back, they whine."
However, it was Santorum who first complained of the crossover voting tactic in January, telling a Minnesota event that "We want the activists of the party, the people who make up the backbone of the Republican Party, to have a say in who our nominee is as opposed to a bunch of people who don't even identify themselves as Republicans picking our nominee."
He called then for closed primaries with only Republicans allowed to take part "because it's the Republican nomination, not the independent nomination or the Democratic nomination."
The exit poll information in Michigan showed one in 10 respondents were Democrats voting in the GOP primary, while six in 10 were Republicans and the rest were independents. More than half of the Democrats backed Santorum, while Romney was ahead among Republicans and the two were tied among independents, the exit polls showed.
Democrats who voted Tuesday said they didn't need much convincing to support Santorum in order to weaken Romney.
Bruce Fealk said he voted for Santorum because "he's by far the weakest candidate."
The idea is to help Obama get re-elected, Fealk said, adding: "We want Mitt Romney to go bankrupt in Michigan."
Romney attributed Santorum's late rise in the polls to his recent "incendiary comments" about Obama.
"We have seen throughout the campaign that if you are willing to say really outrageous things that are accusative and attacking of President Obama, that you are going to jump up in the polls," Romney said. "You know, I am not willing to light my hair on fire to try and get support. I am who I am."
The tough talk reflected the high stakes in Michigan. Romney has led nationwide polls off-and-on over the course of the campaign, but has been unable to increase his support base. Santorum is the latest of Romney's rivals to challenge him for front-runner status by playing on conservatives' reservations about the former Massachusetts governor.
Santorum's hat trick earlier this month propelled him to a lead in national polls and a double-digit lead in Michigan two weeks ago. But he had a lackluster performance in last week's CNN/Arizona Republican debate and has fallen into a statistical tie with Romney in national polls and in Michigan.
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Both candidates have been spending most of their time in Michigan following the last debate, and Republican strategist and CNN contributor Alex Castellanos said a Romney victory there would greatly boost his campaign.
"In Michigan, Romney has brought Santorum down from a double-digit lead to a few points in his wake. If Romney wins in Michigan, there will be no opponent left he hasn't defeated one-on-one," Castellanos said earlier in the day.
"In the year of the comeback, it may turn out that the king of the comebacks is Mitt Romney," said Castellanos, who was a top media adviser for Romney's 2008 nomination bid but who is not taking sides this cycle.
Michigan and Arizona come four days before Washington state holds its caucuses on Saturday and a week before 10 states hold primaries and caucuses worth 437 delegates on Super Tuesday.
"If Romney wins Michigan, he can suffer a few losses on Super Tuesday and still take the nomination," Castellanos said.
Meanwhile, Santorum adviser John Brabender, who has been downplaying expectations for his candidate in Michigan, noted that the 30 delegates at stake there are proportional, so a second-place finish with a decent delegate haul is just as good as a win.
To Brabender, Santorum already has won by forcing Romney to spend major campaign resources in a state considered home turf.
"The Romney campaign is spending a fortune they never expected to spend in Michigan, and every dollar they spend in Michigan is a dollar they don't have on Super Tuesday," Brabender told CNN on Monday.
For Gingrich, it's all about Super Tuesday and Georgia, which he represented in Congress for more two decades.
"I want to focus on winning in Georgia. I think it is essential to us to do that, and we are going to do everything we can between now and next Tuesday to win here at home," Gingrich said last weekend while campaigning in the state.
However, Gingrich's hopes of building a strong support base in the South after his lone victory in South Carolina appears in trouble. Santorum holds a big lead in polls in Tennessee, another Super Tuesday state.
Paul, the libertarian champion making his third bid for the White House, campaigned briefly in Michigan to try to win some delegates, but was mostly looking ahead to Washington state and Super Tuesday caucuses to try to increase his delegate count.
"We'll continue to work in the caucus states" where investments of time and resources pay off in delegates, Paul told CNN on Tuesday night.