Santorum said Sunday he could do "exceptionally well" in Michigan, the next state to host a presidential contest, along with Arizona, on Feb. 28, and where Romney's father was governor.
"We're going to spend a lot of time in Michigan and Arizona, and those are up next. And that's where we've really been focusing on," Santorum told ABC's "This Week." He suggested that a strong showing in those contests would make the presidential contest "a two-man race," dismissing current rivals Newt Gingrich and Ron Paul.
Santorum shrugged off his third-place finish Saturday in caucuses in Maine, where he didn't actively compete. He described Romney's recent criticism - Romney is painting Santorum as a longtime Washington insider who pursued home-state projects - as "desperate."
"You reach a point where desperate people do desperate things," said Santorum, a former representative and senator from Pennsylvania.
Romney captured Maine, state officials reported Saturday night, ending a three-state losing streak to Santorum. Santorum defeated Romney in Colorado, Minnesota and Missouri on Tuesday.
There won't be another election until Arizona and Michigan and the next debate is 10 days away.
That's an unusually long break in a rapid-fire Republican race that featured six contests in the last two weeks alone. Romney and his rivals now have 17 days to raise cash and bolster their organizations for what's shaping up to be a long slog to the Republican nomination and the right to face President Barack Obama in November.
As Santorum eyes Romney's home state, Romney turns his attention to extending the huge cash advantage he enjoys over his rivals.
He left Maine to attend a West coast fundraiser Saturday night and issued a written statement to mark his victory in the low-turnout contest.
"I'm heartened to have the support of so many good people in this great state," Romney said. "The voters of Maine have sent a clear message that it is past time to send an outsider to the White House."
He's expected to spend much of next week courting fundraisers, while sprinkling in a handful of campaign events. He'll be in Arizona Monday evening.
In Maine, Romney won just a plurality of the vote, suggesting he still has much work ahead to unite GOP voters behind his candidacy.
Former Alaska Gov. Sarah Palin, a prominent voice among some conservatives, said Romney has work to do to convince GOP voters he's moved beyond his "pretty moderate past ... even in some cases a liberal past."
"I am not convinced, and I do not think the majority of GOP and independent voters are convinced," Palin said on Fox News Sunday.
Romney has been focusing increasing attention on social issues in recent days, perhaps with that goal in mind. He has been particularly aggressive in criticizing Obama's recent decision regarding contraception.
On Friday, after three weeks of controversy that pitted the nation's Catholic bishops against the White House, Obama revised his policy. Instead of requiring employers to cover contraception, the policy would now require insurance companies to provide free birth control coverage in separate agreements with workers who want it.
White House chief of staff Jack Lew defended the decision Sunday, noting that there is longer room for compromise.
"This is our plan," he said on CNN's "State of the Union."
The focus on social issues plays well for Santorum, who has long been considered a staunch cultural conservative. Those credentials helped fuel his success last week.
But he wasn't a factor in Maine, where Romney narrowly defeated Paul, capturing 39 percent to Paul's 36 percent of the vote, according to state Republican chairman Charlie Webster. Santorum and Gingrich, who didn't actively campaign in Maine, won 18 percent and 6 percent respectively.
Coming off last week's success, Santorum saw a surge in donations - reporting bringing in $3 million over the three days immediately after last week's hat trick - but is unlikely to catch Romney in the money race.
Santorum reported just $279,000 in the bank at the end of December, compared with $19.9 million for Romney. Gingrich had $2.1 million, but is still carrying substantial debt, while Paul reported $1.9 million.
Romney's relative success in Maine - combined with his victory in the presidential straw poll at the Conservative Political Action Committee conference in Washington hours earlier - may help enhance his cash advantage, despite some lingering skepticism among some conservatives.
The Maine vote totals reflected about 84 percent of the state's precincts. The contests scheduled for the coming days - including an entire county that postponed its caucuses because of a snow storm - will not be counted, according Webster, the state GOP chairman.
"We're not going to even accept the ballots. No one's going to keep track of them," he said, noting that those were the rules established by the party.
Romney's campaign has demonstrated skill and flexibility in winning a big state like Florida and eking out a victory in a low-turnout contest like Maine, where organization and voter contact are essential. Out of Maine's 258,000 registered Republicans, nearly 5,600 cast ballots in the weeklong voting.
But questions about Romney's durability as his party's presumed front-runner persist. Fully 61 percent of Maine voters selected a candidate other than Romney in a state practically in his backyard. And Romney's showing was down considerably from 2008, when he won 51 percent of the vote.
Speaking to supporters in Portland, Paul expressed disappointment that only a portion of the state's caucuses had counted toward the total.
"I wish all the caucuses had met today," Paul said, adding, "It's almost like we could call it a tie."
Romney won 11 delegates and Paul won 10, according to an analysis by The Associated Press. Santorum and Gingrich were shut out.