DES MOINES, Iowa (CNN) -- In some polls, immigration ranks behind only the Iraq war and the economy as Iowa voters' top issue.
Rudy Giuliani says his immigration policies in New York created "an orderly, legal, lawful society."
A recent University of Iowa poll found that 58 percent of Republican voters consider the issue very important.
Republican candidates are trying to convince those voters that they are the ones to fix immigration as they head into the nation's first contest in the presidential primary season.
Iowa's meatpacking industry has become a magnet for illegal immigrants and the impact on taxpayers regularly makes headlines.
Iowa Republicans say the issue can make or break a campaign.
Republican caucus voter Tammy Ramey said it is her top issue. Watch what effect the immigration issue will have on the Iowa vote »
"I would lean towards a candidate who is very firm on his positions on immigration," she said.
A Romney mailing slams Giuliani's so-called "sanctuary cities" policy when he mayor of New York, which prevented city workers from reporting illegal immigrants at schools and hospitals.
On Monday, Giuliani went to the Mexican border to promote his support for a "virtual fence" and to defend his immigration policies in New York, calling them "The most successful in the history of the country in creating an orderly, legal, lawful society."
Back in Iowa, Romney pounced on that.
"Instead of distancing himself from sanctuary policies as mayor, [he] said that the sanctuary illegal alien policies he had when he was mayor made his city more lawful, orderly and legal," Romney said. "That is turning reason on its head."
Giuliani's campaign distributed data saying illegal immigration went up in Massachusetts when Romney was governor.
New York was worse, Romney fired back.
"In every possible way I could think of we were tough on illegals, welcoming legal immigration, but ending illegal immigration," Romney said.
The tit-for-tat between the candidates and their campaigns on their immigration records is not likely to let up as the January 3 caucus nears. E-mail to a friend