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AURORA — Before 20,000 supporters who braved long lines and cold temperatures and stayed late into the night Sunday, President Barack Obama made the case for a second term at his final Colorado campaign rally ever.

“After four years, Colorado, you know me,” Obama said late Sunday night, in his 13th visit to Colorado this year. “You know what I believe, you know where I stand, you know I’ll tell the truth. You know I will fight for you every single day.”

This critical swing state, which played such an important role in his historic journey to the presidency four years ago, remains one of the closest electoral battlegrounds.

As they criss-crossed the swing states Sunday, both presidential candidates, in their final stump speeches, continued to wrestle over the mantra of “real change.”

“I know what real change is because I’ve fought for it, because I’ve delivered it,” Obama said. “I’ve got the scars to prove it.

“So after all we’ve been through together, we can’t give up now.”

As he did during a rally in Boulder Thursday, Obama ran through a laundry list of first-term accomplishments: rescuing the auto industry, saving the country from a second Great Depression, Wall Street reform, the killing of Osama bin Laden, the end of the Iraq War and the repeal of Don’t Ask, Don’t Tell.

The latest polls show the candidates tied or with leads well within the margin of error in Colorado, which the president carried by nine points over Sen. John McCain in 2008.

Sunday night, Obama campaign members were confident about getting to 270 electoral votes, based largely on their small but significant lead in Ohio; but the campaign still views Colorado as one of four states — Virginia, Florida and New Hampshire are the others — that are still too close to call.

The large crowd gathered Sunday afternoon, as lines of supporters several-thousand people long snaked all across the Lowry campus.

Roughly an hour before Obama took the stage, the singer Dave Matthews took the stage and played a short acoustic set.

With temperatures dipping into the thirties, Obama took the stage just before 11 p.m. clad in a fleece jacket.

As he’s done at every rally since returning to the campaign trail Wednesday, Obama began his remarks with a unifying message about the country coming together after Hurricane Sandy devastated the New Jersey coast.

But here, in the city he last visited following this summer’s deadly theater shooting that left 12 dead, Obama fine-tuned his lines.

“Unfortunately, the people of this town understand what it is to grieve more than most because of that horrible shooting,” Obama said. “Just as you begin to heal as a community, we’re going to help our friends on the East Coast heal as well. We’re going to walk with the people whose lives have been upended, those who have lost loved ones; we’re going to walk with them every step of the way on the hard road ahead because that’s what we do as Americans.

“We will carry on with a spirit that says, ‘No matter how bad a storm is, we come back. No matter how tough times are, we will thrive’.”

Obama also framed his economic plan, which calls on the wealthiest Americans to pay higher taxes, as a carbon copy of President Bill Clinton’s, reminding the crowd of the economic growth of the 1990s.

And, as he wrapped up his remarks, an increasingly raspy president encouraged supporters to work hard for him in the last two days of the campaign, to protect the change he’s fought for and secure him a second term.

After Mitt Romney rallied 17,000 supporters Saturday night at Comfort Dental Amphitheater in Englewood, the GOP ticket maintained a presence in Colorado on Sunday, with vice presidential nominee Paul Ryan rallying a crowd of 1,100 supporters in Douglas County.

Ryan has a final Colorado rally at Johnson’s Corner in Larimer County on Monday.