Hickenlooper said the state didn't immediately need outside help. The problem was reaching the most critical areas.
Rescuers have been frustrated by debris, impassable roads and mudslides, Pelle said.
"This is not your ordinary disaster," Pelle said. "All the preparation in the world, all the want-to in the world, can't put people up those canyons while debris and walls of water are coming down."
The rain started falling in earnest about 6 p.m. Wednesday and continued into Thursday, sometimes at the rate of about an inch an hour, according to radar estimates. That added up to about 6 to 7 inches of total rainfall.
"The rain, it almost feels like hail, the drops are so thick," University of Colorado Boulder student Ryan Colla told CNN affiliate KUSA. "It just keeps coming and coming, and when you think it's going to subside, it starts to rain down harder."
The sudden influx of water turned Boulder Creek -- which runs through the campus and other parts of the city bearing its name -- into a high, fast, muddy and dangerous torrent, Colla told the station.
"It freaked us out," he said.
At its peak, Boulder Creek was flowing at 16 times its normal rate for this time of year, city spokeswoman Sara Huntley said.
But that was not the only stream causing trouble, Pelle said. Unlike the last devastating flood in Boulder in 1969, this storm caused virtually every waterway in the area to overflow, he said.
Water rushed through Aurora, east of Denver, swirling and breaking like an ocean hitting a beach. CNN affiliate KCNC captured video of one person stumbling dangerously while trying to cross an Aurora street and finally struggling at the edge of the water. Three onlookers pulled that person to safety.
In Estes Park in Laramie County, KCNC video showed the Big Thompson River rushing above both sides of a bridge and flooding several small businesses.
And rain is likely to continue to pose problems, CNN meteorologist Chad Myers said.
"It could rain again all night," he said.
Dams threatened, roads washed away
Between 25 and 30 roads were closed Thursday afternoon in Boulder County, Prentup said.
Several roads washed away, including one near Lafayette -- about 12 miles southeast of Boulder -- where rescue crews staged the dramatic rescue of a man from an overturned, partially submerged car.
Lafayette Fire Chief Gerry Morrell said it appeared three cars driving through pre-dawn darkness and heavy rain plunged into the void left when water washed out the road. Two other motorists got out of their cars, at least one with the aid of firefighters.
At first, rescuers feared the last car's occupant may have died after more than 30 minutes in the partially submerged car, Morrell said.
The rescue -- captured live on television -- nearly went awry when the car, which had been pulled up so that it was on its side, turned back onto its roof in the swift water just as the man was preparing to climb through a window broken open by his rescuers.
"I was aghast," said Morrell, who watched the rescue unfold from the riverbank.
All three people were taken to a hospital for treatment of minor injuries, according to fire officials.
A firefighter in Boulder had to climb a tree to escape the initial surge of water. Although injured, the firefighter made it to a nearby home, Prentup said.
In Lyons, water was flowing over the tops of five dams, Boulder County spokeswoman Gabi Boerkircher said. The dams had not broken, but emergency officials were monitoring them very closely, she said.
The extent of the damage was widespread but difficult to pin down, Pelle said.