WASHINGTON (AP) ― Mitt Romney’s uninspiring showing in Super Tuesday’s primaries nonetheless moves him closer to the Republican presidential nomination. But a string of events and voter data underscore his challenge in winning independent voters turned off by the long, divisive primary.

Romney won a tight race against Rick Santorum in Ohio, where he heavily outspent his main rival, and posted victories in Massachusetts, Virginia, Vermont , Idaho and Alaska. Tuesday’s mixed results will not change Republican operatives’ conviction that Romney is the likeliest nominee. He still has the most delegates, money, organization and experience. His opposition remains divided among three rivals.

“I’m going to get this nomination,’’ Romney told supporters before Ohio’s results were known.

Santorum, Ron Paul and Newt Gingrich show no signs of dropping out, however. Santorum won Tennessee, Oklahoma and North Dakota and Gingrich easily won his home state of Georgia. The results will give them and Paul enough encouragement to keep running for weeks, if not months.

As long as the contest continues, Romney must cater to the staunchly conservative voters who dominate Republican primaries and caucuses. And that’s a problem for the former Massachusetts governor.

Heavy attention to the social issues that excite many conservatives is often distasteful to independents and centrists. They are the crucial voters who will decide whether President Barack Obama gets a second term in November.

The past week has been especially worrisome to Republican insiders. National debate focused on Republicans’ challenges to birth control, conservative radio commentator Rush Limbaugh’s verbal attack on a female law student, and what some Democrats call a Republican “war on women.’’

Romney tried to stay above the fuss. But his tardy and wan critique of Limbaugh’s crass remarks describing the female law studient as a “slut” and “prostitute” didn’t quiet his detractors, to the delight of Democratic activists.

Many Republican campaign veterans shrug off polls that show a dearth of Republican enthusiasm for Romney. Conservatives will rally behind the eventual nominee this fall because ousting Obama is their top goal, these strategists say.

But Romney’s drop in esteem among independents is “the thing that’s going to take some time to fix,’’ said Terry Nelson, who was political director for the Bush-Cheney 2004 campaign.

A recent Wall Street Journal-NBC News poll suggested the hard-fought Republican contest is having a corrosive effect on many Americans, including independents. Forty percent of adults said the Republican primary has given them a less favorable impression of the party. Six in 10 independents used negative terms when asked to describe the party’s nominating process.

The same poll found Obama’s approval rating at 50 percent, his highest level in 10 months, as more people expressed confidence in the economy.

Such findings may help explain the bounce in Obama’s step Tuesday as he faced reporters at the White House. The president poked gentle fun at the Republicans’ contest before turning serious, and scolding.

While the Republican candidates are “popping off’’ about a possible war with Iran, Obama said, he is the one who absorbs the costs of troops wounded or killed in battle. “Those folks don’t have a lot of responsibilities,” Obama said dismissively.

Romney benefits from Republican voters who are tired of the intra-party squabbling and who see him as having the best chance to beat Obama.

Romney “has less baggage than the others, and more money to help him against Obama,” said Don Ryan, 71, who voted Tuesday in a Cincinnati suburb. He said he wishes other Republicans had run, and he’s not sure Romney is a true conservative, but he wants the matter settled. “I was ready for it to be over in November,’’ Ryan said.

Exit polls of Ohio Republican voters contained bits of good news for Romney. He did relatively well among voters who seem engaged in the fall campaign’s likely chief themes: those who are fed up with government and see the economy and the deficit as top concerns. He and Santorum roughly split these so-called tea party voters.

Still, Santorum led easily among social conservatives. Born-again or evangelical voters gave him a double-digit lead over Romney, who is Mormon.

These voters may grouse if Romney is the nominee. But they’ll get over their hurt and “rally behind Romney,’’ said long-time Republican consultant Charlie Black, who informally advises Romney’s team. “Obama is the great uniter among Republicans,” he said.

Republican consultant Matt Mackowiak said Romney is lucky that “Santorum and Gingrich will continue to foolishly split the conservative vote.”

“But their continued campaigning costs Romney money and time, sends independents heading for the hills, and imperils Romney’s chance to win in the fall,’’ he said.

Independents will be Romney’s biggest challenge this fall, if he wins the nomination. That’s especially true if Democrats succeed in their bid to paint the Republican candidates as badly out of step on issues such as women’s access to birth control.

Black said independent voters tend to decide late in the process. That will give them about six months to compare Obama with Romney ― if Romney is the nominee ― and the economy will be the big issue.

Even if the economy continues its slow improvement, Black said, millions of Americans will still be unemployed, underemployed or no longer seeking work. The independent voters who swung heavily to the Republicans in the 2010 mid-term elections care deeply about jobs; “Obamacare,” the health care reform pushed through by the president;a the federal debt and a big-spending government, Black said.

“There are plenty of ways to keep jobs and the economy front and center,” he said, and those issues play to Romney’s strengths.

Black and other Republican campaign veterans will sleep better, however, when their contest ends and they can start training all their voters’ ire on Obama.