WASHINGTON – Heading toward the final week of a long campaign, President Obama and Republican Mitt Romney are locked in a neck-and-neck contest, with Obama scrapping like a challenger and Romney campaigning like a president.

National and swing state polls are inconclusive, and a host of intangibles are likely to sway the outcome: Who will turn out? How do people feel in their gut about the economy? And is there a real “October surprise” that will give one candidate a last-minute shove across the finish line?

One potential game changer: The government will report the latest unemployment numbers next Friday, the last report before Election Day four days later.

The final push is likely to mean an unprecedented blur of messages to Americans in about a dozen contested states — on TV, in the mailbox, in Twitter accounts and email inboxes — while Americans in the rest of the country will watch almost as bystanders, their states leaning solidly toward one candidate or the other.

Romney heads into this last stretch trying to motivate voters with lofty generalities and an appeal to patriotic instincts.

Think big, the former Massachusetts governor implores audiences. The economy’s weak, but I’m a turnaround artist and I’ll fix it. He ends speeches by quoting lines from “America the Beautiful.”

“Our campaign is about big things, because we happen to believe that America faces big challenges,” he told an Ames, Iowa, audience Friday. “This is a year with a big choice, and the American people want to see big changes. And together we can bring real change to this country.”

Obama talks big, too, but he also spends lots of time tearing into Romney, sometimes in unusually blunt language for the normally cautious Obama. “A bullshitter,” he said of Romney in an interview with Rolling Stone released this week.

Obama’s campaign this week put together a 20-page “New Economic Patriotism” booklet. The campaign is running ads and telling crowds that Romney would return American society to the ugly old days.

“You can choose to turn back the clock 50 years for women and immigrants and gays, or in this election, you can stand up for that basic principle enshrined in our founding documents that all of us are created equal,” Obama said Thursday in Cleveland.

“All of us (are) endowed with certain inalienable rights by our creator … it doesn’t matter whether you’re black or white, Hispanic, Asian, Native American, young or old, rich or poor, gay or straight, abled or disabled,” he said.

In state after state, the race comes down to the same variables: Who voters think can best manage the economy, and who will show up at the polls.

The economy grew at a sluggish 2 percent pace in the last quarter, and unemployment remains historically high. Largely as a result, Obama’s approval rating flirts with the magic 50 percent mark.

The best clue to the race’s trajectory in these last days is the candidates’ travel. According to RealClearPolitics, a nonpartisan website, the contest is now in a virtual tie in 11 states. Romney and Obama plan to spend the first part of this week in Ohio, Colorado, Iowa, Florida and Wisconsin.

The states to watch, though, could be those where a candidate seemed assured of victory but finds the polls suddenly tightening. An Obama or Romney visit to Michigan, Arizona or Pennsylvania would suggest those states are now in play.

Michigan and Pennsylvania have long been seen as safe Obama states. But RealClearPolitics has both in the “tossup” category, as polls show Obama’s lead is between 4 and 5 percentage points.

Should Obama start to pull away, the states to watch would be Arizona and North Carolina. Arizona has long been a Republican stronghold. But the president might have a chance if Latino voters turn out in big numbers, said Earl de Berge, editor of the Phoenix-based Rocky Mountain Poll. “There’s real anger in the Latino community” over restrictive, Republican-backed immigration policies, de Berge said. His Oct. 4-10 survey found Hispanic voters favored Obama by a 77 percent to 10 percent margin.