"This is not a coronation," Brownback said in a telephone interview with The Associated Press. "People have the right to vote, and let's let Iowans choose. I am going to participate in the Ames straw poll."
Romney called it "a gift" when Rudy Giuliani and John McCain bowed out of the straw poll on Wednesday. The former Massachusetts governor said his fellow front-runners realized "they couldn't keep up with me in the first state in the presidential sweepstakes."
Brownback challenged Romney and others to debate before and during the straw poll.
Brownback, the Kansas senator, is less well-known, but he is popular among conservatives who influence the Iowa caucuses and had hoped for a strong showing against top-tier candidates.
"I'd hoped to do very well," he said. "We've got a good organization in Iowa and a strong ground game. I think we were in a position to do quite well, and I think that's why they pulled out."
Giuliani, the former New York city mayor, and McCain, an Arizona senator, are skipping the August straw poll but maintain they are still competing in the state's caucuses, the first in next year's GOP nomination process.