9:30 PM UPDATE: Romney wins Republican presidential primary in Ohio.
8:50PM UPDATE: Mitt Romney wins the Republican presidential caucuses in Idaho.
But his rivals countered crisply. Rick Santorum won in Tennessee, Oklahoma, and North Dakota, while Newt Gingrich scored a home-field win in Georgia -- fresh evidence that they retain the ability to outpace the former Massachusetts governor in parts of the country despite his huge organizational and financial advantages.
Romney and Santorum also dueled in Ohio, their second industrial-state showdown in as many weeks and the marquee matchup of the busiest night of the race.
In Ohio, with 15 percent of the precincts counted, Santorum had 38 percent, Romney 36 percent, Gingrich 15 percent and Paul 8 percent.
Win or lose there, Romney said "I think we'll pick up a lot of delegates, and this is a process of gathering enough delegates to become the nominee and I think we're on track to have that happen."
There were primaries in Virginia, Vermont, Ohio, Massachusetts, Georgia, Tennessee and Oklahoma. Caucuses in North Dakota, Idaho and Alaska rounded out the calendar.
In all, 419 delegates were at stake in the 10 states, and Romney's early wins allowed him to pad his earlier lead for the nomination.
He picked up at least 64 during the evening, Gingrich 23.
That gave the former Massachusetts governor 264 in The Associated Press count, while Santorum had 92, Gingrich 56 and Paul 25. It takes 1,144 to win the nomination at the Republican National Convention this August in Tampa, Fla.
In interviews as voters left their polling places, Republicans in state after state said the economy was the top issue and an ability to defeat Obama was what mattered most as they made their Super Tuesday choices.
They also indicated nagging concerns about the candidate they supported, even in Massachusetts, There, one-third of all primary voters said they had reservations, and about three-quarters of those voted for Romney.
Massachusetts is a reliably Democratic state in most presidential elections, but in Ohio, 41 percent of primary voters said they, too, had reservations about the candidate they supported. No Republican has ever won the White House without capturing Ohio.
Gingrich's victory was his first since he captured the South Carolina primary on Jan. 21, and the former House speaker said it would propel him on yet another comeback in a race where he has faded badly over the past six weeks.
Obama, the man they hope to defeat in November, dismissed the almost-constant criticism of his foreign policy efforts and accused Republicans of "beating the drums of war" over Iran. "Those folks don't have a lot of responsibilities. They're not commander in chief," he said. Unopposed for the Democratic nomination to a second term, he stepped into the Republican race with a Super Tuesday news conference at the White House, then attended a $35,800-a-ticket fundraiser a few blocks from the White House.
Ohio was the day's biggest prize in political significance, a heavily populated industrial state that tested Santorum's ability to challenge Romney in a traditional fall battleground. Georgia, Gingrich's home political field, outranked them all in the number of delegates at stake, with 76, a total that reflected a reliable Republican voting pattern as well as population.
Romney, the leader in the early delegate chase, flew to Massachusetts to vote and said he hoped for a good home-state win.
He also took issue with Obama, saying, "I think all of us are being pretty serious" about Iran and its possible attempt to develop nuclear weapons.
Gingrich effectively acknowledged he had scant Super Tuesday prospects outside Georgia, where he launched his political career nearly three decades ago. Instead, he was pointing to primaries next week in Alabama and Mississippi, and he told an audience, "With your help, by the end of next week we could really be in a totally new race."
The polls show the president's chances for re-election have improved in recent months, as the economy has strengthened, unemployment has slowly declined and Republicans have ripped into one another in the most tumultuous nominating campaign the party has endured since 1976.
The former Massachusetts governor campaigned into Super Tuesday on a winning streak. He captured the Washington state caucuses last Saturday, days after winning a little-contested primary in Arizona and a hard-fought one in Michigan. He won the Maine caucuses earlier in February.
The victories helped settle his campaign, which was staggered when Santorum won a pair of caucuses and a non-binding Missouri primary on Feb. 7.
Santorum and Gingrich have vied for months to emerge as the sole conservative alternative to Romney, and they battered him as a moderate who would lead the party to defeat in November.
But Romney, backed by a heavily financed super PAC, countered Gingrich's victory in the South Carolina primary with a comeback win in Florida. Last week, it was Santorum's turn to fall, as Romney eked out a win in Michigan after trailing by double digits in some polls 10 days before the primary.
Santorum's recent rise has translated into campaign receipts of $9 million in February, his aides announced last week.
Even so, Romney and Restore our Future, the super PAC supporting him, outspent the other candidates and their supporters on television in the key Super Tuesday states.
In Ohio, Romney's campaign purchased about $1.5 million for television advertisements, and Restore Our Future spent $2.3 million. Santorum and Red, White and Blue, a super PAC that supports him, countered with about $1 million combined, according to information on file with the Federal Election Commission, a disadvantage of nearly four to one.
In Tennessee, where Romney did not purchase television time, Restore Our Future spent more than $1 million to help him. Santorum paid for a little over $225,000, and Winning our Future, a super PAC that backs Gingrich, nearly $470,000.
In Georgia, where Gingrich acknowledged he must win, the pro-Romney super PAC spent about $1.5 million in hopes of holding the former House speaker below 50 percent of the vote, the threshold needed to maximize his delegate take.
While the day boasted more primaries and caucuses than any other in 2012, it was a shadow of Super Tuesday in 2008, when there were 20 Republican contests.
There was another big difference, a trend away from winner-take-all contests to a system of allocating delegates in rough proportion to a candidate's share of the popular vote.
Sen. John McCain won eight states on Super Tuesday in 2008 and lost 12 to Romney and Mike Huckabee combined. But six of McCain's victories were winner-take-all primaries, allowing him to build an insurmountable delegate lead that all but sealed his nomination.