Rep. Jason Chaffetz squirmed in his chair as comedian and satirist Stephen Colbert's questions turned to the topic of illegal immigration.

Chaffetz, then a youthful 41-year-old Republican from Utah, had essentially won his seat in Congress six months earlier, in June 2008, when he ousted Rep. Chris Cannon in a heated GOP primary. Chaffetz had tacked hard right on immigration matters. He bored in on Cannon, a six-term incumbent, for serving as President George W. Bush's point man on a failed immigration overhaul that included a path to citizenship for those here illegally.

No amnesty — no way, no how — was Chaffetz's platform. He wanted illegals rounded up, detained, and deported. His rhetoric was so severe that, while still a candidate, he drew a rebuke from a House member from California who had been forced into a Japanese internment camp during World War II.

"When," Colbert asked Chaffetz, "did rounding up people you don't like in your country and putting them in camps get a bad name?"

Chaffetz parried the question. "I want to enforce the law," he said, flashing a grin.

Tough talk on illegal immigration has been a political winner in the rock-ribbed conservative Utah in recent years. Chaffetz's rise is a case study in its effectiveness.

But quietly and quickly, Utah's demographic terrain is shifting. The state's Latino population leaped by 78 percent between 2000 and 2010. Signs of the boom are everywhere, with Spanish-language media outlets taking hold, ethnic marketplaces sprouting up, and established chains stocking their shelves with Hispanic groceries and goods.

The trend is hardly confined to Utah. Between 2002 and 2010, almost exactly half of the nation's congressional districts, 217, saw their white share of the population plunge by at least 5 percentage points. And in 50 districts, the minority share grew by at least 10 points. Latinos were the driving force behind much of the shift in state after state.

In Utah, however, the growing Latino population's clout in the state's economy has not been matched in the political marketplace. "We're not voting yet — as much as we could be voting, as much as we should be voting," said Tony Yapias, executive director of Proyecto Latino de Utah, an advocacy group for immigration reform. That, too, could be starting to change. For the first time this year, Salt Lake County, the state's most populous, will be required to print voting materials in Spanish.

Cannon, the defeated ex-congressman, didn't mince words about the state of affairs in Utah. He said that the Latino population has surged enough to be seen — it's now at 13 percent — but not yet enough to be heard.

"A lot of people in Utah got threatened by them and that threat got exploited," Cannon said, recalling his ouster. He predicted a coming "backlash to the backlash" against his fellow Republicans for taking "distorted, perverted, weird, and stupid" hard-line positions on immigration.

Chaffetz strongly disagreed. He insisted that he and the GOP can win over both sides — Latinos and the hard-liners — by trying to "fix legal immigration," the nation's byzantine maze of visas, wait lists, and regulations.

Now 45, Chaffetz is young enough to care not just about Utah's present, in which a forceful stance on illegal immigration is still the path to power in the GOP, but also about its growing Latino future. He is the kind of keen political operator who became chief of staff to the state's former governor, Jon Huntsman, while still in his 30s. And his early record in Congress on immigration issues is more nuanced than the caricature Colbert was creating, or even that his original campaign's rhetoric suggests.

He has not wavered from his tough immigration stands in Washington, but his emphasis has shifted. In a recent interview, Chaffetz didn't mention deportation or detention until directly asked.

"It's not all simply about locking down the border," he said. "You can build the fence as far and wide as you want, but unless you fix legal immigration, you'll never solve the problem."

He has devoted one of his full-time aides to "deal almost exclusively with immigration cases" of constituents, Chaffetz said. And as a lawmaker, he has delved into the complexities of the immigration code, authoring the only substantive piece of immigration legislation that has advanced through either chamber of this Congress with bipartisan support. The measure, now stalled in the Senate, aims to reform the per-country quota system for highly skilled worker visas.

"Everybody's frustrated with the visa system," Chaffetz said. His measure passed the House by 389-15.

It's the kind of effort that he said he can sell in his district, which stretches across the central and western swaths of Utah into the urban areas just south of Salt Lake City. It's a region that saw its white share of the population dip by 7 percentage points in the past decade.

Utah mapmakers have dramatically redrawn Chaffetz's district, starting next year. But, in many ways, the boundaries matter less than the demographic wave that is washing across the state — and the country. In 1990, Latinos in Utah numbered 84,500; by 2010, they totaled 358,000, and their share of the population had nearly tripled.

Whites still dominate Utah politics. Chaffetz's current district remains 77 percent white. But the burgeoning Latino population is pushing itself into the political conversation, even if it hasn't yet formed as powerful a voting bloc as it has in parts of neighboring Arizona or farther west in California.

The story is similar almost everywhere. In Idaho, Republican Sen. Mike Crapo has advertised bilingual office hours with his Spanish-speaking staff. The Republican National Committee, meanwhile, recently dispatched Latino-outreach experts to six states, including North Carolina and Virginia, hardly historic hotbeds of Hispanic voters.

Minorities now make up at least one-third of the population in more than 200 congressional districts. That number is steadily climbing — in Chaffetz's district, in Utah, and across much of the country.

Shane Goldmacher is a National Journal correspondent.