Presidential travel, especially in an election year, offers an insight into the favored electoral road map. So it is no surprise that President Obama’s post-State of the Union schedule includes traditional battleground states:

Iowa, Nevada, Colorado, all of which John Kerry lost in 2004 but Obama picked up four years later. Michigan, historically Democratic but also the home state of a certain potential Republican nominee.

But Arizona?

Other than 1996, when Bill Clinton beat Bob Dole, Arizona hasn’t voted for a Democrat for president since Harry Truman in 1948. It has two Republican senators and a Republican governor — and, judging by the 2010 results, the trend lines aren’t promising for Democrats.

In that last election, the state’s congressional delegation flipped from five Democrats and three Republicans to five Republicans and three Democrats. The state Legislature went redder still.

So, Arizona?

The Obama campaign, which played no role in the upcoming trip, insists that it is serious about making a play for the state. It argues that Arizona would have been within reach four years ago were it not for the fact that the Republican nominee, John McCain, was the state’s senior senator.

Arizona’s historical voting patterns notwithstanding, the campaign argues, the state’s fast-changing demographics make it a logical — if far from certain — target for a Democratic pickup. Hispanics now constitute almost 20 percent of the voting-age population.

“I’m all about the numbers,” campaign manager Jim Messina told me in a conversation before the president’s travel plans were announced. “If you just close your eyes and don’t say it’s Arizona, and look at the sheer numbers . . . in our lifetime Arizona is going to be a blue state. The question is when. We don’t say we’re definitely going to get Arizona to turn blue, but we’re going to take a long and hard look at it.”

In a sense, the Obama campaign’s interest in Arizona and its 11 electoral votes may be a flirtation born of necessity. It reflects the grim likelihood — actually, make that the near-certainty — that the Democrats will be unable to hold on to many of the traditionally Republican prizes they seized in 2008, states such as Indiana, North Carolina and Virginia.

If Obama wins, his victory likely will not — certainly not against Mitt Romney — be by the comfortable margin of four years ago.

The insight of the Obama 2008 campaign, however, was to imagine an expanded electoral playing field in which the road to Democratic success did not hinge on winning in Ohio and Florida. Arizona is a logical extension of that theory.

Running against Romney in Arizona, for example, Democrats will relentlessly broadcast his vow to veto the “Dream Act,” which would provide a path to citizenship for children of illegal immigrants, and — in a state with one of the highest foreclosure rates in the nation — Romney’s statement that housing prices should be allowed to hit bottom.

“Of all the states out there with low-hanging fruit, Arizona is leaps and bounds ahead of any other state,” said a Democratic official. “This isn’t a state where you have to draw an inside straight to be successful.”

Campaign officials point to recent Democratic wins in mayoral races in Tucson and Phoenix. And they see opportunity in the retirement of Republican Sen. Jon Kyl. Obama, not usually one to dabble in recruiting congressional candidates, personally reached out to Richard Carmona, surgeon general under President George W. Bush, to persuade him to seek the Democratic nomination.

Republicans discount the notion of a Democratic pickup, noting that Democratic voter registration in the state now lags behind that of Republicans and independents.

“Obama can come to Arizona all he wants,” said Shane Wikfors, communications director for the Arizona Republican Party. But of a win in November, Wikfors said, “That’s not going to happen. The momentum is in our direction — a very engaged Republican base and very disgruntled independent voters.”

There is, no doubt, an element of shake-up-the-other-side bravado in the Obama campaign’s advertised interest in Arizona. At the very least, proclaiming that Arizona is on the campaign’s target list could pressure the Republican nominee to spend money there.

Yet the possibility of Democrats raiding Arizona underscores the longer-term difficulty faced by Republicans: how to remain competitive, given the twin realities of the growing Hispanic electorate and a party whose increasingly strident anti-immigration message is turning off that very voting bloc.

“Texas is definitely going to go purple,” Messina said. “In the next 10 years, you’re going to spend time in Texas reporting on presidential campaigns.” Now that would be wild.