Romney, who has called President Obama too inexperienced, declined to answer a Fox News reporter's question about whether Rubio, 40 and in his first Senate term, was qualified to serve a heartbeat away from the presidency.
"I don't think I have any comments on qualifications for individuals to serve in various positions in government in this stage," Romney said. "That's something we're going to be considering down the road as we consider various potential vice presidential nominees."
For his part, Rubio smiled and said, "I'm not talking about that process anymore." In a forum last week, he had said, "If I do a good job as vice president" - before apologizing and correcting himself to say "as a senator."
Republicans in four other Northeastern states are also voting Tuesday: Delaware, New York, Connecticut, and Rhode Island. Since Romney has effectively clinched the nomination, he has been seeking to appeal to the broader audience he will need to win the general election, and the "veepstakes" speculation has grown louder.
Rubio, a favorite of antitax tea party activists, is the first potential running mate Romney has campaigned with since sewing up the nomination. Many GOP strategists believe adding the Cuban American to the ticket could shore up Romney's standing among Hispanics, the fastest-growing bloc of swing voters. That could help him in battleground states such as Pennsylvania, where Hispanics have nearly doubled since 2000.
Romney trails Obama by more than a 2-to-1 ratio in most recent polls among Latino voters; a Pew Research poll this month, for instance, found 67 percent of Hispanics backing Obama to 27 for Romney.
During the GOP primary battles, Romney, a former governor of Massachusetts suspected of being a moderate in some quarters of the conservative base, took a harsh line on illegal immigration. He said he would have vetoed the proposed DREAM Act, which offers children brought here illegally a path to citizenship. He also came out against in-state tuition for children of undocumented immigrants and supported Arizona's controversial crackdown on illegal immigration as a model for the nation.
Immigration is seen as a litmus test for many Hispanic voters, but the Obama campaign notes that the health-care-access law the president pushed through Congress is also hugely popular, with as many as 45 percent of Latinos lacking health insurance. Romney has vowed to repeal that law.
On Monday, Rubio described how his parents came from Cuba five decades ago with little education or knowledge of English and became successful, giving him the chance to go the Senate because of "the privilege and the honor of being born in the single greatest society in all of human history."
He argued that Obama and the Democrats were in danger of stamping out what makes America special by stoking the politics of envy.
"We now have a leader in this country who wants to take that from us," Rubio said, "who's telling Americans that the reason why they're hurting is that other people are doing too well. That the way they can climb up the ladder is to pull other people down. If we do that, we become like every other country in the world."
Romney said at the news conference that he was considering Rubio's recent immigration-overhaul proposal, which would provide visas for children who were brought to the country illegally, rather than creating a "new class of citizenship," as he said the DREAM act would do. He declined to endorse it outright.
With an eye toward November, Romney said he "fully supports" Obama's push to keep lower interest rates on Stafford student loans, breaking with GOP congressional leaders and even some of his own past statements.
If Congress does not act by July 1, interest rates on Stafford Loans are due to increase from 3.2 percent to 6.8 percent. This week, Obama is talking up a freeze on those rates as he visits three battleground states - North Carolina, Colorado, and Iowa.
"I support extending the temporary relief on interest rates for students - in part because of the extraordinarily poor conditions in the job market," Romney said Monday. He was walking away from the news conference when he came back to the microphone to make the comment on the student-loan issue.
Lis Smith, a spokeswoman for the Obama campaign, contended Romney's promise was meaningless, given his support for budget proposals that would make deep cuts in other education programs. "The numbers just don't add up," Smith said.
After hearing Monday's speeches, Bruce Downing, 73, of Lima, said Romney had proven himself through the primary process and would make a strong nominee - especially if Rubio becomes the vice presidential candidate.
"I know I'm excited, and I think the people in this room were excited," Downing said. "His charisma would really add a plus to the ticket."
Contact Thomas Fitzgerald
at 215-854-2718 or email@example.com, or on Twitter @tomfitzgerald. Read his blog, "The Big Tent," at www.philly.com/bigtent.