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President Obama kept up his campaign of put-downs Tuesday, as Mitt Romney accused his opponent of going full-bore negative, with the candidates charging out of their final debate and into a narrow band of hotly contested battlegrounds.

Those states, four of which were hit by the campaigns Tuesday, will play host to the final, bruising two weeks of the 2012 race. And with no debates or even fundraisers left on the calendar, all that's left is a barrage of ads and stump speeches that will try in part to build on the debate momentum -- and, of course, get out the vote.

“These debates have super-charged our campaign,” Romney said during an afternoon rally in Henderson, Nev.

Romney also repeated one of his top lines from the Monday night debate -- that Obama’s attacks on him are “not an agenda” to improve America. He also argued again that Obama has instead resorted to gimmicky phrases like “Big Bird,” “Romnesia” and “binders full of women.”

In Ohio, Obama repeated the "Romnesia" line and argued, as he did the night before, that Romney wanted to let the U.S. auto industry to go bankrupt.

“If you say you are a car guy but you wrote an article titled ‘Let Detroit go bankrupt,' you definitely have a case of Romnesia,” the president said.

That's Obama's way of summing up his charge that Romney has forgotten what his own positions have been on the issues. "Don't worry," Obama quipped. "ObamaCare covers pre-existing conditions. We can fix you up. We can cure this disease."

Obama started with a morning rally in Del Ray, Fla. before heading to Dayton, Ohio, with Vice President Joe Biden, who was at the University of Toledo earlier in the day.

In Nevada, which has one of the country’s most prolonged and highest unemployment rates, Romney promised to cut the state’s 11.8 percent jobless rate at least to 6 percent.

“But if we’re going to see that kind of recovery, we're going to need real change,” he said.

Running mate Paul Ryan introduced Romney in Nevada by asking those in attendance whether they saw the debate.

“We saw Governor Mitt Romney offer this country bold ideas in leadership,” Ryan said. “Obama failed to lay out an agenda and decided his path to re-election is to distort, distract and win by default.”

After Nevada, Romney and Rep. Ryan attended a rally in Colorado with musician Kid Rock and New Mexico Gov. Susana Martinez.

Residents in the battleground states -- which include Virginia and to a lesser extent Pennsylvania and Wisconsin -- will for the final two weeks of the race be barraged by ads and campaign stops by the candidates and their surrogates.

Setting the tone for the day, Romney's campaign released a TV ad Tuesday morning hammering the president's so-called "apology tour" overseas in 2009. It includes the line: "You went to the Middle East and you flew to Egypt and to Saudi Arabia and to Turkey and Iraq. And ... you skipped Israel, our closest friend in the region."

No matter who wins, it appears highly unlikely that Obama will get anywhere close to the 365 electoral votes he won in 2008. It takes 270 to clinch the presidency, and this year's contest could be historically close, judging by recent polls.

For months, the electoral map has appeared to favor the president, with more states considered safe Democratic territory than safe Republican territory. But Romney's surge in the polls has changed the map. The Associated Press estimates that Obama is likely to win at least 237 electoral votes to Romney's 191, with 110 electoral votes up for grabs.

By contrast, the RealClearPolitics map last week gave Romney the advantage for the first time. The latest projection shows Romney with 206 likely electoral votes, and Obama with 201. Their map shows 131 electoral votes up for grabs across 10 states.

It's no accident that those 10 states are largely on the itinerary -- repeatedly -- of both campaigns for the next two weeks. They include the four states the campaigns were hitting Tuesday.

On Wednesday, the schedule gets even more chaotic for the Obama campaign, with the president setting out on a two-day, six-state blitz. He'll hit Iowa, Colorado and California on Wednesday, followed by Florida, Virginia and Ohio

The campaigns are, naturally, using their running mates to cover more ground.

While Romney hits Nevada and Iowa on Wednesday, Ryan will make a swing through Ohio.

Each campaign has its own variations on a path to 270 electoral votes -- but Ohio, Florida and Virginia are considered among the most important. Florida is the biggest, with 29 electoral votes. Ohio has 18 and Virginia has 13 -- Obama won all three in 2008.

Recent polling in Ohio shows Obama either up by a hair, or tied with Romney. In Florida, Romney seems to have the edge. Virginia is a dead heat.

But states like Iowa, Pennsylvania, Wisconsin and New Hampshire are also vital. North Carolina, a state Obama won in 2008 and where the Democrats held their convention this year, has long since trended toward Romney and is considered by some analysts a likely pick-up for Romney next month.