Yet there's one issue neither man is expected to go near: gun control.
Even with the hot-button issue of gun control back in the national spotlight after 12 people were killed in Friday's movie-theatre shooting rampage in Aurora, Colo., it's not expected to elbow its way into presidential politics.
Indeed, the White House's only remarks in the aftermath of the carnage in Aurora have been to say the president backs the country's existing laws — even though the alleged gunman in the Colorado shootings legally acquired various weaponry, including an assault rifle and 6,000 rounds of ammunition purchased online.
"(Obama) believes we need to take steps that protect Second Amendment rights of the American people but ... ensure that we are not allowing weapons into the hands of individuals who should not, by existing law, obtain those weapons," White House press secretary Jay Carney said over the weekend.
"The president's view is that we can take steps to keep guns out of the hands of people who should not have them under existing law. And that's his focus right now."
Obama clearly has political reasons for steering clear of gun control. His standing is low among white working-class voters — big believers in the Second Amendment's right to bear arms — and he can't afford to alienate them further ahead of November's presidential election.
And it's not as though he risks offending large swaths of the American public with his refusal to talk tough about gun control.
There are an estimated 270 million guns in the hands of U.S. citizens, making the country the most heavily armed nation on Earth on a per capita basis.
Polling suggests the American public has grown increasingly resistant to tougher gun control legislation over the past two decades, with many states loosening laws to the extent that their citizens can carry weapons in public.
Gun sales are booming, with 2011 breaking records for gun purchases; the numbers for 2012 are expected to soar even higher. An estimated 50 per cent of American households now contain guns.
Both Obama and Romney have learned lessons from those who have waded into the debate before them, said William Schneider, a well-known American political analyst and public policy professor at George Mason University — gun control is a no-win issue, no matter how passionately gun control advocates clamour for it.
"Sometimes in the past, these types of shootings have lead to legislation, but it ends up getting reversed and then the gun lobby turns out in great numbers and votes against anyone who voted in favour of it," Schneider said.
"We're not having the conversation because essentially the gun control forces have learned that it doesn't go anywhere. The gun lobby is too powerful."
One Democratic senator, Frank Lautenberg of New Jersey, plans to bring back a bill he introduced in 2010 after former congresswoman Gabrielle Giffords was shot in the head in another mass shooting spree.
The legislation, which would ban high-capacity gun magazines that allow gunmen to fire off multiple rounds in quick succession, has never gone anywhere in the Senate.
Both the alleged Colorado gunman — who made his first court appearance Monday — and the man who fired on Giffords were carrying magazines.
"We need to start today on efforts to prevent the next attack," Lautenberg said in a statement.
"No sportsman needs 100 rounds to shoot a duck, but allowing high-capacity magazines in the hands of killers ... puts law enforcement at a disadvantage and innocent lives at risk."
But most congressional Democrats, many of whom are privately in favour of tougher gun control laws, haven't forgotten what happened in 1994, when they passed legislation outlawing assault weapons.
Two months later, Democrats got pummelled in the mid-term elections, with former president Bill Clinton insisting the gun lobby played a major role in their historic defeat. The assault weapons ban was allowed to expire in 2004.
What's more, Schneider said, in 2008 the U.S. Supreme Court deemed the Second Amendment an individual right that cannot be infringed upon by government. That ruling was considered a significant victory for the gun lobby, and means any politician tackling the issue today is tackling the U.S. Constitution — a daunting and unappealing task.
The National Rifle Association, meantime, keeps up the fight.
"When they tell you that a government ban on certain firearms will somehow make you safer, don't you believe it, not for a second, because it's a lie just like the lies they've told you before," Wayne LaPierre, the CEO of the NRA, told a recent gathering of the organization.
"Their laws don't work."
How has the NRA, with just four million members, become so formidable?
"A few years ago, what the NRA had going for it was intensity," Schneider said. "They had a passionate constituency that communicated to politicians very efficiently, with the message: 'If you go against us on this law, we will come after you.'"
Because that constituency is made up of single-issue voters, they've chipped away at the support base of politicians. How? The majority of Americans don't vote according to gun laws alone — voters who are in favour of gun control, in other words, will cast their ballots against a pro-gun control politician if they don't like his or her stances on other issues.
"They impressively organized the constituency that cared about the issue above anything else, and they made it a voting issue," Schneider said.
Today, the NRA is a well-oiled machine. The Washington Post recently estimated that the NRA succeeded in helping elect four out of every five candidates it endorsed in 2010's mid-term elections.
In recent months, the might of the NRA was evident when the House of Representatives voted to hold Attorney General Eric Holder in contempt of Congress for withholding documents pertaining to the so-called Fast and Furious program.
Fast and Furious allegedly put guns in the hands of Mexican drug lords; gun advocates suspect the federal government did so in order to argue for tougher gun control laws stateside.
Seventeen Democrats voted in favour of censuring Holder after the NRA threatened to withhold support for their campaigns if they didn't. Politicians of all stripes, indeed, are well aware that the NRA can make or break them.
The lobby has also been so successful, many believe, because guns and a mistrust of big government are such an integral element of the American psyche.
Noted historian Richard Hofstadter's seminal essay, "America as a Gun Culture,'' delved into the country's enduring affection for firearms because they're so closely tied to its history. American settlers were pioneers and revolutionary rebels, and guns are therefore considered central to the American identity, particularly in the south and the West.
Schneider said many Americans still fervently believe that they need to be armed against the government in case it decides to "come and get you," noting that gun advocates still consider the ill-fated government raid on Waco, Texas, in 1993 to have been an assault on both freedom of religion and gun ownership.
And he predicted so-called Obamacare, Obama's sweeping health-care legislation recently upheld by the U.S. Supreme Court, will play a role in future standoffs.
"Within a few years, I have no doubt you're going to see a few characters holed up in a cabin in northern Michigan with a lot of guns to say: 'I ain't buying no health insurance; let the government come and get me.'"