Paul Ryan and Obama were vying for headlines and attention in Iowa, where the president decisively won his first primary victory in January 2008 on his way to snagging the Democratic nomination.
Romney and Obama are neck and neck in the polls in the so-called Hawkeye State less than three months before the presidential election.
But polls also suggest Romney's choice of Ryan — a Wisconsin congressman and the Republican party's fiscal restraint czar — hasn't wowed the American public.
Ryan was described as a "fair" or "poor" choice by 42 per cent of respondents to a USA Today/Gallup survey released Monday, while 39 per cent of respondents said they viewed him as an "excellent" or "pretty good" vice-presidential choice.
Romney pollster Neil Newhouse said in a statement that the findings simply reflect the fact that Ryan, the chairman of the House of Representatives budget committee, isn't yet a household name in the United States.
However, previous USA Today/Gallup surveys taken immediately following a vice-presidential pick have yielded more favourable ratings for running mates. Only Dan Quayle, George H. W. Bush's No. 2 in 1988, had lower ratings.
Ryan was heckled Monday during his first stop at the Iowa State Fair in Des Moines, where a year ago, Romney famously confronted his own hecklers by saying, "Corporations are people, my friend."
Protesters, including two women who attempted to rush the stage carrying a banner, repeatedly interrupted Ryan's remarks. The women were removed from the event by state troopers.
"It's funny because Iowans and Wisconsinites like to be respectful of one another and peaceful with one another and listen to one another," Ryan said. "These ladies must not be from Iowa or Wisconsin."
Another male protester then began chanting: "Stop the war on the middle class." He, too, was removed.
Democrats have reacted with glee to Romney's choice, swiftly pouncing to portray Ryan as an extremist for his proposals to overhaul Medicare, a beloved government program that guarantees access to health insurance for Americans over 65.
Conservatives, on the other hand, have lauded Romney for making a bold choice by tapping an innovative thinker who has long insisted the party needs to present big, transformative ideas to the American people.
On Sunday, Ryan said he and Romney intend to "split up" often and campaign separately in order to "double our efforts."
Looking every inch the "mini-Mitt" in his first joint interview with Romney on "60 Minutes," where both men sported blue blazers, checked shirts and well-tended hairstyles, Ryan once again said politics has been a calling for him.
"I've felt for a while now that our country is in a very perilous situation," said Ryan, a 42-year-old, seven-term congressman.
"And I've done everything I could in my career as chairman of the budget committee to try and make a difference, to tackle this economic and fiscal challenge before it tackles us."
Both men denied suggestions that the Romney campaign had effectively turned the presidential campaign into an ideological battle rather than a referendum on Obama's first term.
Pundits on both the right and left alike have argued that the focus of the campaign will now shift to Ryan's controversial budget proposals, once branded "right-wing social engineering" by fellow Republican Newt Gingrich during his own run for president.
Indeed, a web video released Monday morning by Obama's re-election team focuses on Ryan's Medicare proposals.
"Medicare is a boon to senior citizens," one woman says in the ad, filmed in Florida — a crucial swing state that's home to millions of seniors.
"And without that we choose between food and going to a doctor."
In his "60 Minutes" interview, Ryan seemed well-prepared for that line of attack, telling CBS's Bob Schieffer that his own mother is "a Medicare senior in Florida" while emphasizing he's not proposing to reform the program for those already receiving benefits.
Instead, Ryan said, his proposals would shift Medicare over time to a voucher-based system aimed at "preserving" the entitlement program.
As he campaigned in Florida on Monday, Romney assured voters that he and Ryan "want to make sure we preserve and protect Medicare."
Obama welcomed Ryan to the campaign trail on Sunday, calling him a "decent man" but also an "articulate spokesman for Gov. Romney's vision."
"It's a vision," the president added, "that I fundamentally disagree with."
On Monday, Obama's campaign doubled down, branding Romney-Ryan economic proposals "the same top-down economic scheme that crashed our economy and devastated the middle class in the first place."
At his own campaign event Monday in Iowa, Obama assailed Ryan for his opposition to a proposed federal farm bill that would provide disaster relief to farmers and ranchers in the Midwest, currently enduring the worst drought in 50 years.
"I am told that Gov. Romney's new running mate, Paul Ryan, might be around Iowa the next few days — he is one of the leaders of Congress standing in the way," Obama said in the town of Council Bluffs as the crowd booed in response.
"So if you happen to see Congressman Ryan, tell him how important this farm bill is to Iowa and our rural communities. We've got to put politics aside when it comes to doing the right thing for rural America and for Iowa."
Obama was also scheduled to appear at the Iowa State Fair later Monday, while Vice President Joe Biden was campaigning in North Carolina, another crucial battleground state.
Romney, meantime, kicked off a bus tour today in Florida with Sen. Marco Rubio, a Cuban-American lawmaker who was himself once considered a potential VP pick but was ultimately deemed too risky a candidate due to the party's anti-immigration base.
In St. Augustine, Romney called Ryan "a man who has proven that he knows how to solve problems."Suggest a correction