Mitt Romney's come-from-behind win in his native Michigan, and his easy victory in Arizona, are obviously good news for the former Massachusetts governor. But they won't resolve the knottiest problems vexing the Republican Party's presidential race, which has become angrier in recent weeks.

Romney landed no knock-out punch on Rick Santorum, the fiery social conservative who loves to remind everyone how difficult Romney finds it to excite and unify the party's base. Nor is it likely the GOP contest will ease its emphasis on social issues, such as Catholic birth-control doctrine, which gives President Barack Obama a clearer lane to highlight the slightly improving economy.

With 99 percents of precincts reporting, Romney earned 41 percent of the Michigan primary votes, while Santorum had 38 percent.

In Arizona, Romney earned a more convincing victory, garnering 47 percent of the vote to Santorum's 27 percent.

Romney's victories Tuesday avert a huge embarrassment and offer some comfort to Republicans who think he has the best chance to attract independent voters and disaffected Democrats this fall. Romney, however, is far from able to start saving his campaign money and focusing fully on Obama.

Santorum has made high-profile visits to Ohio, Tennessee and other states voting in next week's Super Tuesday primaries. Former House Speaker Newt Gingrich didn't compete in Michigan, but he also remains in the race, appealing to his own slice of Republicans who crave more conservative red meat than Romney dishes out.

Gingrich, bolstered by another big contribution from Las Vega casino owner Sheldon Adelson, hopes to do well in Tennessee and Oklahoma, and to win Georgia, which he represented in Congress for 20 years. Like Santorum, he routinely denigrates Romney's Massachusetts record.

Gingrich this week called Romney a "pro-choice, pro-gun-control, pro-tax-increase governor."

"I don't believe a moderate can beat President Obama," Gingrich said.

Libertarian-leaning Rep. Ron Paul of Texas is still running, too.

Romney remains the strongest, best-organized and best-financed Republican in the race. Many GOP insiders find it hard to envision anyone else winning the nomination. But he continues to underwhelm, and campaign reporters can search for days without finding a voter truly passionate about Romney.

Romney's landslide Arizona victory handed him 29 delegates in that winner-take-all state. He was expected all along to win Arizona, however, where a sizeable Mormon electorate helped him, and Santorum made only modest efforts.

Romney's Michigan win, meanwhile, prevented a likely panic among his backers. Partisans will argue whether his margin was impressive, with fans noting that he trailed Santorum in early polls. Still, Romney was born and raised in Michigan, where his father was a top auto executive and three-term governor.

As he did against Gingrich in Iowa and Florida, Romney undercut his toughest challenger - this time, Santorum - with brutal TV attack ads financed by a super PAC that raises millions of dollars. The ads indulge in the sort of fact-fudging hyperbole that infuriates the target's supporters and makes the entire campaign sometimes seem petty and joyless.

One ad, for instance, suggests Santorum wanted to let felons vote in federal elections, a distortion that clearly rankles the former Pennsylvania senator.

As Michigan Republicans were voting Tuesday, Romney acknowledged that clumsy allusions to his wealth have sometimes hurt him, and he expressed calm about his strengths and weaknesses. He also accused Santorum of dirty tricks, citing automated phone calls that urged Democrats to vote for Santorum in the open primary.

These spats may be forgotten by the fall. An economic downturn, soaring gasoline prices or a crisis in Iran might cripple Obama.

But establishment Republicans would rest easier if the intraparty sniping abated and Romney showed an ability to inspire GOP voters of all stripes to coalesce behind him.

Veteran Republican strategist Terry Holt said Romney clearly has work to do but has proven again that he "rises to the occasion when he has to."

Indeed, Romney has a pattern of hauling down his chief rival - Gingrich in Iowa, then Florida, and now Santorum in Michigan - with lulls in between, allowing Gingrich to carry South Carolina and Santorum to win Minnesota and Colorado.

Holt said "the road only gets steeper and narrower and more expensive" from here for Santorum, Gingrich and Paul.

"There's no question they have work to do on the base," Holt said of Romney's team. "But Barack Obama is going to do a lot of that work for us." He said Romney can win the loyalty of hard-core conservatives as long as he shows them respect and "gives voice to the anger and frustration they feel."

Santorum and Gingrich will keep stoking that anger, perhaps for several months. Eventually, however, one of them must knock off Romney in a state as significant as Michigan if he is to be denied the nomination.