These days, the question is not how to grow, but how to pay for all these new people. Roads are crumbling, schools are starved for funds, and rural communities say all this metro-area expansion is sucking them of water and money.

“You rest on your laurels at your own peril,” said Mr. Hickenlooper in an interview at the state’s gold-domed Capitol. His fear, he added, is that “we will strangle on our success.”

Of course, not everyone is interested in solutions put forth by Democrats like Mr. Polis, which include a change to a longstanding state law that limits the amount of tax revenue the state can collect. “It’s worse than moving blue,” said Jon Caldara, who leads the Independence Institute, a Denver-based libertarian think tank. “We’re turning into California.”

The best-known Republican candidate, Walker Stapleton, 44, the state treasurer, is promoting himself as a supporter of the president’s tax plan while promising to yank funds from sanctuary cities. Apparently hoping to avoid scrutiny ahead of the primary — he has three lesser-known challengers — he has skipped some debates and repeatedly dodged reporters.

When he does appear, he often saves his fire for Mr. Polis: “The issues that matter are: What is Jared Polis going to do to the economic future of Colorado?” he said.

But a Polis primary victory is far from certain, despite the $11 million the congressman has poured into his own campaign.

His Democratic challengers include Cary Kennedy, 50, a former state treasurer who would be the state’s first female governor if elected; and Mike Johnston, 43, a Spanish-speaking former state senator and principal who once ran a school in a juvenile prison.