The party establishment is coalescing behind the former Massachusetts governor, with top Senate Republican Mitch McConnell saying Romney was all but certain to be the party's nominee to run against Obama in November.
Wins on Tuesday in Wisconsin, Maryland and the US capital Washington would likely push Romney past the halfway mark in terms of the number of delegates he needs to clinch the presidential nomination at the party convention in August.
In the tightest race, in Wisconsin, where Romney and main rival Rick Santorum campaigned on Monday, Romney holds a 7.5-percentage point lead in polls, according to the RealClearPolitics website.
Romney spent much of Monday chastising the Democratic incumbent and his "government-centered society" for failing to lead a recovery out of a deep recession and "crushing" the American dream.
Romney also made it clear he was operating as the presumptive nominee.
Obama would "try to have people disqualify our nominee which will probably be me instead of talking about where we've been and where we're going as a nation," Romney told a crowd in Green Bay, Wisconsin.
While most signs point to Romney as the party's eventual flag-bearer, it gets cloudier looking beyond the pitched battle for the nomination, with a new USA Today-Gallup poll released Monday showing him trailing Obama.
The poll has Obama leading 49 to 45 percent over Romney nationally among registered voters in a hypothetical one-on-one matchup, the largest lead to date in Gallup polling.
Obama's lead in 12 swing states was even greater, with the president ahead 51-42 on average in key states like Florida, Ohio and Pennsylvania.
That marks a dramatic shift in fortunes for Obama, who a month ago trailed Romney by two percentage points in swing states.
The numbers also showed waning enthusiasm among Republican voters.
"The decline is especially apparent among Romney voters, whose enthusiasm has fallen 13 percentage points from January, and now is on par with Obama voters' enthusiasm," Gallup researchers reported.
Former Democratic president Bill Clinton, who prevailed in his own bruising nomination battle 20 years ago and went on to win the White House, said he doubted Romney can turn around his fortunes in the general election.
"Mr Romney has a different challenge than I did," Clinton told ABC News.
"We never had to change what we were saying from primary to the general. The problem that governor Romney has, is his character attack was 'You don't really know what he believes. He did this, he says that'."
Romney has faced stubborn skepticism by conservative voters, who fear that the former governor of liberal Massachusetts will tack to the left once he wins the nomination in order to appeal to independents.
That scenario is fodder for Santorum, a strong critic of abortion and gay rights who has tapped into conservative angst about the frontrunner, insisting Americans need a candidate "whose policy is written on his heart."
But McConnell said Romney "is going to be an excellent candidate, and I think the chances are overwhelming that he will be our nominee."
"It is in the best interest of our party to get behind (Romney) and make the case against the president of the United States."
Santorum, a former Pennsylvania senator, insisted the race was "a lot closer than Mitt Romney and the pundits are spinning" in an interview with CNN, referring to a string of more conservative state primaries scheduled for May.
He has insisted his performance should be judged in light of Romney's far greater campaign spending, saying: "We've done a great job in taking the seven loaves and fishes and turning it into 11 state wins."
Romney meanwhile tore into Obama before a crowd in Milwaukee, saying: "What this president's doing regulation after regulation new tax after new tax is slowly but surely crushing the dreams and the dreamers."
Romney has won 21 out of 34 contests so far and amassed some 565 delegates, and after Tuesday he will likely have more than half the 1,144 delegates needed for the nomination.
Santorum has racked up 11 victories but has less than half Romney's delegate count.