Americans should not expect the war in Iraq to be wrapped up quickly as violence and instability will likely continue, a U.S. governor said Tuesday during a visit here with three other state governors.

But Arkansas Gov. Mike Huckabee said the Sunni-led insurgency was losing momentum even though insurgent attacks rose over the past year.

Huckabee flew into Baghdad from neighboring Kuwait City with Wisconsin Gov. Jim Doyle, Texas Gov. Rick Perry and Wyoming Gov. Dave Freudenthal. The four met U.S. troops and were briefed by military commanders on the state of the rampant insurgency. Perry and Huckabee are Republicans and Doyle and Freudenthal are Democrats.

"A light bulb burns very brightly right before it goes out," Huckabee said of the insurgency during his first trip to Iraq. "The insurgents know they have everything to lose if democracy continues."

But he also asked for patience from the American public.

"For us to expect that this is going to be rock solid and peaceful is unrealistic," Huckabee said. "Americans are impatient people. We are a people who like things solved quickly."

About 4,000 Arkansas national guardsmen are in Iraq, said Huckabee, who visited Baghdad and Tikrit during his two-day visit to Iraq. He was scheduled to fly on to Pakistan, Afghanistan, and then to Belgium for a visit with NATO officials.

Doyle told CNN that he was impressed with the high morale of the American soldiers he met during his prearranged trip to Iraq, despite threats of suicide and roadside bombings and other attacks that they face each day.

"The troops have a very high morale and are very committed to the mission, and I think would very much agree with that definition," said Doyle.

About 2,000 Wisconsin National Guards forces are serving in Iraq and Kuwait.

Asked whether Wisconsin had enough forces to deal with any emergency with so many troops outside the state, Doyle said at least 8,000 were still at home and capable of dealing with any crises that may arise.

"But that's not to say this doesn't put an enormous drain on us," Doyle said. "It is what it is. We are very proud of our leadership of the National Guard who have managed this very difficult time very, very effectively."

Perry, from President Bush's home state, told FOX News that he sees progress in Iraq.

"Obviously you're not going to rebuild a country overnight, but I think this is going along very well," Perry said.

The governors' trip to Iraq and Kuwait was arranged by the Department of Defense to provide the state leaders with an idea of the conditions under which American forces are serving.