Mitt Romney won both of Tuesday’s Republican presidential primaries, routing Rick Santorum in Arizona and narrowly securing Michigan, his birth state.

The victories will provide an important boost for Romney, a former Massachusetts governor who has sought to cast himself as the GOP’s inevitable nominee. He has now won primary contests in six states: New Hampshire, Florida, Nevada, Maine, Michigan and Arizona.

“We didn’t win by a lot, but we won by enough. And that’s all that counts,” Romney told supporters Tuesday night in the Detroit suburb of Novi.

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He said nothing about Santorum in his speech, instead criticizing President Obama at length and trying to boil down a complicated economic message.

“I’m going to deliver on more jobs, less debt, smaller government,” Romney said. Later, he returned to another three-point message about government: “I’ll make it simpler, smaller and smarter.”

Santorum and former House speaker Newt Gingrich (Ga.) have won a total of five states. On Tuesday night, Santorum cast the close outcome in Michigan as a sign of success, noting that it came in Romney’s “back yard.”

“A month ago, they didn’t know who we are, but they do now,” Santorum told supporters in Grand Rapids. “The people of Michigan looked into the hearts of the candidates, and all I have to say is ‘I love you back.’ ”

Santorum avoided the kind of incendiary rhetoric that has drawn criticism in recent days — including an attack on Obama for suggesting that young people should go to college. Instead, Santorum talked about small government and praised the women in his family for their hard work at home and in their careers. He spoke about how his mother had gone to college and received at least one advanced degree.

Romney’s victories on Tuesday are unlikely to solve the larger problems that have held back his campaign. Even after months of work and millions of dollars spent, he has not won over a vast swath of Republicans.

That was clear from Michigan exit polls, which showed that Santorum had beaten Romney decisively among important Republican blocs. The former senator from Pennsylvania held a 15-point lead among voters who identify themselves as “very conservative,” a 40-point edge among those who say they want their candidate to be “a true conservative” and a 41-point advantage among those who want a candidate with “strong moral character.”

Romney, by contrast, bested Santorum among voters who care strongly about beating Obama in November, and among those who say the economy is their chief concern.

He may have been helped by Santorum’s strident stands on social issues in recent days. The former senator called Obama a “snob” for wanting young people to attend college and said that he almost vomited after reading a speech by John F. Kennedy about the separation of church and state. Santorum later said he wished he could take back that statement.

Among his fellow Catholics, Santorum lost to Romney by 43 percent to 37 percent, according to exit polls.

Negativity takes toll

As voting was underway, 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 robo-call in which his campaign urged Democrats to vote for Santorum in Michigan’s open primary.

“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 voters there 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, at the Jan. 3 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 themselves as Democrats in 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 before.

“We’re going to get this economy growing again,” he 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 in Perrysburg, Ohio — that state will vote on Super Tuesday next week — Santorum said Romney had benefited from Democrats and independents in past primaries. He said it was wrong for him to complain about the tactic being used against him.

“That’s what bullies do,” Santorum said. “You hit them back and they whine.”

Romney, who took questions from the media for the first time in three weeks on Tuesday, 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 Michigan campaign headquarters in Livonia.

Among his mistakes, he said, were recent remarks that highlighted his wealth, including a statement that his wife “drives a couple of Cadillacs.”

When reporters asked if those comments had hurt his campaign, he replied: “Yes. Next question.”

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,” he 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.”

The two other major Republican candidates, Gingrich and Rep. Ron Paul (Tex.), did little to contest Michigan or Arizona. On Tuesday night, Gingrich held a rally with at least 500 supporters at the University of West Georgia in Carrollton.

Staff writers Philip Rucker in Livonia, Mich.; Nia-Malika Henderson in Perrysburg, Ohio; and Amy Gardner in Georgia contributed to this report.