BOULDER, Colo. – President Obama beseeched supporters in Colorado on Thursday to stand with him and turn out the vote in a battleground state that has evolved into one of the tightest races in the nation this fall, one that could determine whether Obama wins a second term in the White House.

“They’re counting on you not voting,” Obama said of Republican Mitt Romney’s campaign. “That’s their entire strategy. Colorado, my money’s on you.”

Before a roaring rally of 10,000 supporters at the University of Colorado-Boulder, Obama pressed his case for re-election: That a vote for Romney would amount to an endorsement of favorable and unfair treatment for the wealthy, a lesser status for women and tightened loan rules for college-bound students.

“You’re going to be making a choice between two fundamentally different visions of America,” Obama said. “After all that we’ve been through together, we sure as heck can’t give up now.”

Although Romney has been portraying himself as the outsider who would shake up Washington, Obama disputed the characterization.

“He’s saying he’s the candidate of change,” Obama said. “But let me tell you, Colorado, we know what change looks like.”

Obama’s 12th visit this year to the Centennial State came as a new round of polls suggested the contest here is as tight as ever just days before Election Day.

Obama won Colorado by a margin of 9 percentage points four years ago, but Republican Mitt Romney has targeted the state as a potential GOP pickup because of its weakened economy. Colorado’s unemployment rate is 8 percent, slightly above the national average and 1.6 percent higher than when Obama took office.

“His margins everywhere are going to be slight, if he has any margins at all,” said Eric Sondermann, a Denver-based political analyst, who handicapped the race as “very, very close.”

Colorado has just nine electoral votes and is distant from several of the election’s biggest prizes – including Florida, Ohio, Virginia and Wisconsin – but both campaigns are allocating huge resources here in the contest’s final sprint.

Rep. Paul Ryan, Romney’s running mate, rallied supporters in Greeley, northeast of Denver, on Thursday, and he’ll do a second rally in the state on Friday. Romney will stage two events in Colorado – one near Denver and another in El Paso County, a Republican stronghold – on Saturday, the same day Vice President Joe Biden is set to appear in Pueblo.

And even before Air Force One touched down for Thursday's visit, the Obama campaign announced the president would be back in the region on Sunday for a rally in Aurora, just east of the state capital, as a part of his final push for votes.