LOS ANGELES — President Barack Obama is running statistically even with former Massachusetts Gov. Mitt Romney in 12 key swing states and is slightly ahead of Texas Gov. Rick Perry and businessman Herman Cain, according to the USA Today/Gallup poll released today.

The poll, which looks at both national trends and at the races in what everyone considers to be the 12 battleground states that will likely determine the 2012 election, paints a picture of Obama facing a tougher road to re-election than an incumbent should.

But the president, a Democrat whose approval rating has been in the low 40-percent range in recent months, can take heart from the poll’s findings that he is running better against specific Republican candidates than he does against a generic Republican, indicating that when faced with a real choice, voters seem to prefer Obama to Romney, Perry or Cain.

According to the poll, Obama is tied among national voters with Romney at 47 percent and leads Perry 49 percent to 45 percent. In its first measurement of Cain, the poll found Obama ahead 48 percent to 46 percent. The poll was taken before reports surfaced that two women received financial settlements after complaining that Cain had sexually harassed them.

But overall, the results show all three GOP candidates running strongly against Obama. The national results are based on interviews with 1,056 adults taken Oct. 26-27; the poll has a margin of error of plus or minus four percentage points.

But the American electoral system is based on indirect representation rather than direct democracy. The Founding Fathers feared the unmediated passions of the mob and wanted to ensure that wiser heads would have a greater role. Hence the creation of the presidential electors who actually vote for president based on the popular vote in their home states.

Because of the Electoral College, where a candidate’s support exists is often more important than just how many people back him or her. A candidate needs 270 electoral votes to win, and in 2012, Obama can pretty much count on winning enough states to give him about 196 electoral votes, while the GOP candidate starts with about 191. In the center are 12 states, worth 151 electoral votes for which both parties will spend most of their money and resources fighting. Those states, all won by Obama in 2008, are Colorado, Florida, Iowa, Michigan, Nevada, New Hampshire, New Mexico, North Carolina, Ohio, Pennsylvania, Virginia and Wisconsin.

According to the poll, Romney is at 47 percent to Obama’s 46 percent in those 12 states. Obama does better against Perry, 49 percent to 44 percent and Cain, 48 percent to 45 percent. Those results are based on interviews with 1,334 adults, from Oct. 20 to 27. The poll has a margin of error of plus or minus three percentage points.

The polls generally show that the presidential race is extremely competitive at this point, a year before Election Day and two months before the GOP begins voting for its presidential candidate. But Republicans also have an advantage in the enthusiasm arena, according to the poll.

Overall, 47 percent of swing-state registered voters and 48 percent of all U.S. registered voters said they are extremely or very enthusiastic about voting. But Republicans were more eager both nationally and in the swing states. Nationally, Republicans were ahead 56 percent to 48 percent over Democrats. In the swing states, the GOP was ahead in the enthusiasm race 59 percent to 48 percent.