No Democrat since Bill Clinton in 1996 has carried Arizona. In winning, Clinton received 46.5 percent of the vote against former Kansas senator Bob Dole (R), which looks like something close to the ceiling for a Democrat in the state. The last three Democratic presidential nominees — Al Gore in 2000, John Kerry in 2004 and Barack Obama in 2008 — got 45 percent, 44 percent and 45 percent of the vote, respectively, a remarkably consistent showing that suggests Democrats may be capped around that number. (Also worth noting: In a 2002 open-seat governor’s race, Democrat Janet Napolitano won with 46.2 percent; she did take 63 percent in a non-competitive general election four years later.)

Democrats — from the White House on down — insist that history is an imperfect guide when it comes to predicting the competitiveness of Arizona, because of the rapidly growing Latino population.

According to the 2010 Census, three in 10 Arizonans are Latino, up from roughly 25 percent of the state’s population 10 years ago. In both 2004 and 2008, the Democratic presidential nominee won the Hispanic vote convincingly — Kerry by 18 points, Obama by 15 — but there simply weren’t enough Latinos to counter the strong margins the Republican nominee enjoyed among white voters.

The growth among the Latino population — along with the presence of Carmona, who is Hispanic, and outrage within the community over Brewer’s immigration law — makes Democrats optimistic that 2012 will be different.

Democrats are also banking on moderate white Republicans — particularly women — being turned off by the conservative direction Brewer has taken the state, highlighted most recently by her signing a bill that would effectively defund Planned Parenthood.

All nine voted for Mr. Obama in 2008, only to see Republicans make big gains since then.

Now, with many of those states transformed economically and politically by the recession, they are perhaps even less predictable than they were in past close elections. The disparity in their circumstances highlights the challenges that both the Obama and the Romney campaigns face in framing arguments that will resonate across the country.

It would be hard to argue that these states are better off now than they were four years ago, given that they have yet to recover the jobs they lost. Often, that makes a compelling argument for a challenger trying to unseat an incumbent.

But political scientists have found that past elections have been more influenced by the changes in the economy in the year or two before the election. And a range of economic data provided by Moody’s Analytics shows that all nine states are rebounding and that most now have unemployment rates below the national average. If voters in those states begin to feel the improvement by the fall and the economy does not take a turn for the worse, it could aid the president’s efforts to hold on to enough of them to win.