Mitt Romney has won both of Tuesday’s Republican primaries, beating Rick Santorum in Arizona and winning a narrow victory in Michigan, the state of Romney’s birth. Preliminary results from both states showed Romney ahead at 10: 15 p.m. His lead was 25 points in Arizona, and four points in Michigan.
These victories will provide an important boost for Romney, the former Massachusetts governor who has sought to cast himself as the GOP’s inevitable nominee. He has now won nominating contests in six states: New Hampshire, Florida, Nevada, Maine, Michigan and Arizona.
So far, Santorum and former House Speaker Newt Gingrich have won five states, combined. On Tuesday night, Santorum cast the close outcome in Michigan as a sign of success, noting that it came in Romney’s “backyard.” 
“A month ago, they didn’t know who we are, but they do now,” Santorum said to supporters in Grand Rapids, Mich. He avoided the kind of incendiary religious rhetoric that had hurt him in recent days, talking about small government and praising the women in his family. “The people of Michigan looked into the hearts of the candidates, and all I have to say is, ‘I love you back.’”
Romney’s two victories on Tuesday will not solve his larger problem. Even after months of work and millions of dollars spent, he has not won over a vast swath of Republican voters.
That was clear from exit polls in Michigan. They showed that Santorum had beaten Romney decisively among important Republican blocs. He held a 15-point lead among voters who called themselves “very conservative.” He had a 40-point among those who wanted their candidate to be “a true conservative,” and a 41-point advantage among those who wanted a candidate with “strong moral character.”
Romney, by contrast, beat Santorum among voters who cared strongly about beating President Obama in November, and among those who listed the economy as their chief concern.
He may have been helped by Santorum’s strident stands on social issues in recent days. The former senator (Pa.) declared that Obama is a “snob” for wanting young people to attend college, and said that he almost vomited after reading a famous speech by John F. Kennedy on the separation of church and state. Santorum later said he wished he could take that statement back.
Exit polls also showed that a long, and often negative, primary campaign seemed to have weighed on all GOP voters. Among supporters of both Romney and Santorum, just over four in 10 said they had cast their votes “with reservations.”
As voters went to the polls Tuesday, an unkind race turned positively insulting. Santorum called Romney a “bully,” and Romney called Santorum an “economic lightweight,” who was engaging in political dirty tricks.
In particular, Romney attacked Santorum for a recent “robocall,” in which his campaign urged Democrats to vote for Santorum in Michigan’s open primary. Under the state’s rules, voters registered as Democrats may still vote in the GOP’s nominating contest.
“I think Republicans have to recognize there’s a real effort to kidnap our primary process,” Romney said. “And if we want Republicans to nominate the Republican who takes on Barack Obama, I need Republicans to get out and vote and say no to the dirty tricks of a desperate campaign.”
Early exit polls in Michigan seemed to show that the negative campaigning had weighed on the state’s Republicans. Less than half of Michigan voters said they backed their candidate “strongly.” About one in seven said they made their choice because they dislike the other options, four times the proportion that said so in this political season’s first votes, back at the Iowa caucuses.
The polls also showed that a large number of Democrats had, in fact, crossed party lines in Michigan. About one in 10 of Tuesday’s voters identified as Democrats in early exit surveys. That was a higher figure than in any of the other early GOP contests.
Earlier Tuesday, Santorum defended his efforts to reach out to those Democrats, saying he was seeking to attract the kind of blue-collar voters who had crossed party lines to vote for GOP candidates before.
“We’re gonna get this economy growing again,” Santorum said. That, he said, is “a message that we’re selling to not just Republicans, but Republicans and Democrats. Reagan Democrats, who are the key for us winning Ohio and Pennsylvania and Michigan.”
Speaking Perrysburg, Ohio — in a state that will vote on “Super Tuesday” next week — Santorum said that Romney had benefitted from Democrats and independents in past primaries. He said it was wrong for him to complain about the tactic being used against him.
“Thats what bullies do,” Santorum said. “You hit them back and they whine.”
Also Tuesday, Romney said he believes he would win Michigan. But already, he has seemed to be lowering expectations: In an interview, the former Massachusetts governor told Fox Business Network, “If I were turned down by Massachusetts, where I have lived for the last 40 years and served as governor, that would be a little harder to explain.”
Romney, taking questions from the press corps for the first time in three weeks, blamed himself, not his campaign aides, for what he acknowledged has been a difficult quest for the nomination.
“I’m very pleased with the campaign, its organization. The candidate sometimes makes some mistakes, and so I’m trying to do better and work harder and make sure that we get our message across,” Romney told reporters during a visit to his campaign headquarters here. “In the final analysis, I anticipate becoming the nominee.”
Also Tuesday, Romney conceded to reporters that he had made “mistakes” that had undermined his well-funded, hyper-organized campaign. Among them, Romney said, were recent remarks that highlighted his wealth, including a statement that his wife “drives a couple of Cadillacs.”
“Yes. Next question,” Romney said, when reporters asked if those comments had hurt his campaign.
Romney also made an indirect reference to Santorum’s series of provocative comments on hot-button social issues in recent days, including his remark that President John F. Kennedy’s speech about the separation of church and state made him want to “throw up.” Santorum said in a radio interview Tuesday that he regretted that remark.
Romney said he believes the United States is “one nation under God” and that religion “certainly has a place in the public square,” but that he respects Kennedy’s speech and believes it was an indication of those views. Romney suggested that Santorum was winning the support of the GOP’s most conservative voters with “incendiary,” “outrageous” and “accusatory” comments.
“It’s very easy to excite the base with incendiary comments,” Romney told reporters. “We’ve seen throughout the campaign that if you’re willing to say really outrageous things that are accusatory and attacking President Obama that you’re going to jump up in the polls. You know, I’m not willing to light my hair on fire to try and get support. I am who I am.”
In early exit-poll results from Michigan, about one-third of voters said that the quality they most wanted in a candidate was the ability to beat President Obama in the general election. If that number holds, that would be a drop from previous contests.
Also, just over one-third of voters said that recent debates were an important factor in their choice. As in other early-voting states, more than half of Michigan voters singled out the economy as the most important voting issue.
But the early data also show more than one in seven voters highlighting abortion as a top concern. If that trend continues, this could be the highest level of concern about abortion since the Iowa caucuses — won narrowly by Santorum.
The other two major Republican candidates, Rep. Ron Paul (Texas) and former House Speaker Newt Gingrich (Ga.), did little to contest Michigan or Arizona. On Tuesday night, Gingrich held his own rally, with at least 500 supporters, at the University of West Georgia in Carollton, Ga.
Gingrich taught history and geography at the school in the 1970s, and he began his congressional career representing a nearby Georgia district. On Tuesday, he sought to celebrate that past with a packed ballroom of fans, rock-and-roll music, a bleacher of students standing behind him on the stage -- and no mention of Arizona or Michigan.
Gingrich desperately needs to win next Tuesday’s primary in Georgia, if he hopes to recover his standing as a contender. But there were some troubling signs on Tuesday, even at a Gingrich event earlier in the day.
Even some of the voters sporting “Newt” stickers and professing their fondness for their hometown former speaker said they were not certain they would vote for him next week.
“I’ll always favor Newt over Santorum,” said Lamar Jenkins, 74, a retiree from Dalton, Ga. “But if it looks like Santorum could beat Newt, then I would vote for Santorum.”
Washington Post staff writers Philip Rucker in Livonia, Mich., Nia-Malika Henderson in Perrysburg, Ohio, and Amy Gardner in Georgia contributed to this report.
More from the Washington Post
In Ohio, Fierce Primary Fight May Hurt GOP's Chances in the Fall
Santorum's Failed Pander
Senate Moderate Olympia Snowe Says She Will Retire