Both men are trying to gain the military vote. In the 2008 election, 54 percent of those who said they had served in the military voted for Sen. John McCain, himself a veteran, to 44 percent for Obama, according to exit polls.
More broadly, both sides ended what had been a weekend of political truce in deference to grieving families and victims of the shooting. Obama and Romney returned to raising millions of dollars and taking jabs at each other over jobs, leadership, and security.
A positive campaign "really would be nice," Romney said even as he declared that sentiment over in an interview with CNBC. He blamed Obama for the tenor.
Obama told the Veterans of Foreign Wars he has kept his promises to end the war in Iraq, wind down the conflict in Afghanistan, and go after al-Qaeda leader Osama bin Laden wherever he was hiding. The terrorist mastermind was killed in a raid on Obama's orders.
In every example, Obama poked at Romney without naming him. On Iraq, Obama suggested Romney would have kept forces in the war zone indefinitely. "When you're commander in chief, you owe the troops a plan," Obama said. On Afghanistan, Obama needled Romney for opposing the 2014 timeline for ending the war. "That's not a plan for America's security," he said.
Romney was to get his say before the VFW, too, on Tuesday before setting out for Britain, Israel, and Poland.
Trying to set the expectations for the opponent, Obama campaign officials challenged Romney to offer clear policy ideas during his trip. Romney's travels will be viewed as a measure of how well he can stand up on the world stage. Obama took an even broader trip as a candidate in 2008.
Four years later, Obama said Monday: "We're leading around the world. There's more confidence in our leadership. We see it everywhere we go."
A Romney spokesman, Ryan Williams, countered that Obama had "diminished our moral authority" in the world.
Still in the shadow of the Colorado rampage, both campaigns weighed how to calibrate their tones, and both were keeping their largely negative television ads off the air in Colorado.
Obama spokeswoman Jen Psaki said the president was moved by his visits Sunday with survivors and family members of the victims of Friday's mass shooting outside Denver. Still, she said: "We've got a long way to go. . . . [Obama] knows that he needs to make sure people know what's at stake."
Romney noted that Obama aide David Axelrod had begun the day reminding via Twitter of the campaign's request to see more of Romney's tax returns. "I haven't seen the healthy, important debate coming from the president's team," Romney said. "It's been almost all attack ads on all sorts of peripheral issues."
Romney himself was back at the rhetorical attack, telling donors in California that Obama was "out of ideas and out of excuses."