Brownback argued that the vice president should be able to provide experience and wisdom but subtly criticized the president for relying too heavily on Cheney.
"You need somebody coming in with foreign policy experience so they don't have to depend on the vice president as much," Brownback said.
Texas Rep. Ron Paul had harsher words for the administration, saying that Cheney is more powerful than Bush and that he would support an amendment to define the Vice President's duties.
All but two of Republcan presidential candidates oppose a timetable for withdrawal from Iraq.
Responding to a video question asking the candidates to clarify their strategies for ending the war in Iraq, Rep. Ron Paul came out swinging in support of immediate withdrawal.
"We went in illegally, and we ought to just come home," Paul charged from the podium to scattered audience cheers.
Paul is co-author, alongside Democratic presidential candidate Rep. Dennis Kucinich, of a House resolution to begin immediate withdrawal.
On the opposite end, McCain echoed his support of the president's Iraq strategy.
"We do now have a strategy that is succeeding. We do have a military whose morale is up because they see this success."
"I'm going to be judged by history, not by public opinion polls," McCain said, saying he looked to the generals on the ground to lead the war strategy.
Since the Minneapolis bridge collapse last week, national infrastructure weighs heavily on the national conscience, and assured improvements in this area also came into play.
"The way to do it is to reduce taxes and raise more money," Giuliani said to audience applause.
Citing his time spent as the New York City mayor and taking a dig at the three senatorial Democratic front-runners, Giuliani said he was "against the liberal Democratic assumption that you have to raise taxes to raise money."
Former Arkansas Gov. Mike Huckabee dealt harsher criticism: "[We have] better navigation in our rental cars than we do running the country today."
Taking a not-so-subtle dig at current foreign policy, Huckabee said, "We have to start addressing building this country, and not everybody else's."
Romney said that "growing the American economy" was the core of improving national infrastructure, while McCain chastised congressional pork barrel spending, implying it was a fiscal roadblock to improvements in national infrastructure, and he promised to veto every bill of its kind "that comes across my desk."
With no White House incumbent to lead the campaign season on the Republican side, the contenders have a tough sell in states with early-nominating contests as they set out to claim territory in a crowded candidate pool.
Fighting sagging approval ratings of the Bush administration and growing national restlessness over the war in Iraq, the contenders walk a fine line in trying appeal to both the party base and to moderates eager for change.
Going into the debate and the Aug. 11 Iowa straw poll, Romney leads. =
Senior political report and author of The Note Rick Klein said post-debate, "Mitt Romney came in as the front-runner, and he did nothing today to change that fact."
Klein felt there were "a number of missed opportunities for those in the second tier -- the same folks who needed to make a splash a week before the Ames straw poll."