HENDERSON, Nev. -- President Barack Obama and Republican rival Mitt Romney joined their running mates in rallying thousands of supporters in must-win battleground states Tuesday as they entered the final, frenzied, two-week stretch of the presidential race.

Obama continued with a familiar line of attack, arguing that Romney has shifted positions on key issues to win voters.

“Trust matters,” a shirt-sleeved Obama told a crowd estimated at 9,500 at a park in Dayton, Ohio. “You know, Ohio, you know me. You know I mean what I say and I do what I’m going to do. You know that I will make the tough decision, even when it’s not popular.”

Romney criticized the president for answering Republicans’ charge of having no second-term agenda by distributing a 20-page pamphlet and a new TV ad with already-introduced plans. Romney’s campaign promptly dubbed it a “glossy panic button.”

“That’s why his campaign is taking on water and our campaign is full steam ahead,” the former Massachusetts governor told 6,000 people at an outdoor pavilion in Henderson, Nev. “Attacks on me are not an agenda.”

Obama campaigned in Florida and Ohio. Romney appeared in Nevada before holding an evening rally in Colorado with New Mexico Gov. Susana Martinez and singers Kid Rock and Rodney Atkins. Together, the two campaigns introduced four new ads Tuesday, including a pair in which the men speak directly into the cameras as they make their final pitches to undecided voters in swing states, who’ll determine the winner.

Obama and Romney participated in their third debate Monday night in Florida. It marked their final joint appearance before the Nov. 6 election.

Initial polls found voters split on who won the debate, with the president taking a slight edge. Romney’s stronger performance in the first debate Oct. 3 led to his steady uptick in the polls. He remains ahead in overall national rankings, according to a compilation of surveys by the website RealClearPolitics, though Obama continues to lead in some battleground states, including Ohio, New Hampshire and Iowa.

A new Washington Post-ABC News national tracking poll released late Tuesday found a statistical dead heat with Romney at 49 percent and Obama at 48 percent among likely voters. Nearly all interviews were conducted before the final debate.

In Nevada, Romney and Rep. Paul Ryan, his vice presidential nominee, sought to portray their campaign as picking up momentum as part of “a movement across the country, as people are realizing we can do a better job than the past four years.”

“We can handle two more weeks of campaigning, but we can’t handle four more years of what he’s given us,” Romney said, ticking off unemployment numbers, sinking housing costs and rising gas prices. He said he’d deliver 12 million new jobs, raise take-home pay and cap spending.

“The president’s approach to creating jobs is another stimulus,” Romney said to shouts of derision from the audience. "How’d the first one work out? . . . His vision for the future is a repeat of the past.”

Kevin Kersey, 41, who attended the rally along with his wife and 3-year-old namesake, said he supported Romney because of the candidate’s business experience.

“That’s what we need in that office, a businessman, someone with private-sector experience,” said Kersey, of Henderson, who owns a pool service company. “We need a businessman to run this country.”