"We've been on a steady, slow, but upward trajectory and things are looking good for us," Huckabee said on ABC's "This Week with George Stephanopoulos."
The former Arkansas governor, campaigning in New Hampshire, was leading the GOP field in a Des Moines Register poll released Sunday -- five points ahead of former Massachusetts Gov. Mitt Romney and 16 ahead of former New York Mayor Rudy Giuliani.
A recent mailer from the Romney campaign took Huckabee to task on immigration. Huckabee said he did not favor amnesty or special benefits, and supports enforcing the law and "a federal government that's competent enough to actually secure the border."
Huckabee said he does not support punishing children "because a parent committed a crime or committed a sin," when it comes to educational benefits and eligibility for in-state scholarships and tuition rates -- provided the students meet the requirements.
When asked about ads running in Iowa that stress Huckabee's Christian views -- Romney is Mormon -- Huckabee said he was introducing himself to Iowa voters.
"I believe some things very deeply and they govern my life," he said.