Iowa Republican Caucus attendees overwhelmingly support strengthening immigration enforcement but are also open to reforming the visa system to allow more legal immigration, according to a survey of likely attendees released Tuesday.

Overall, the issue of illegal immigration was low on attendees' priority list, the survey indicated, falling behind job creation, tax reform and spending cuts. Partnership for a New American Economy, a national organization that supports immigration reform, conducted the poll with a group of Iowa Republican leaders.

"This survey demonstrates that while opinions are strong on tough enforcement for illegal immigration, it is not the top-tier, hot-button issue among Republican caucus-goers it's often made out to be," said John Stineman , spokesman for the coalition of Iowa Republicans who are working with Partnership for a New American Economy.

Eighty-two percent of Iowa Republicans — some of the most conservative voters in the country — said they favor tougher immigration enforcement, according to the survey. But they also showed support for proposals to increase opportunities for high-skilled legal immigrants to enter the U.S. workforce and streamline the process for employers to hire foreign workers. Seventy-two percent of people indicated allowing foreign-born students educated in the United States to accept jobs in the United States after graduation was "definitely good" or "worth a try."

Only 16 percent of likely caucus attendees were solidly opposed to proposals to expand legal immigration.

"There is clearly an appetite for working to solve problems with our legal immigration system and Iowa Republicans make the connection that doing so can help grow our economy," Stineman said.

New York City Mayor Michael Bloomberg said the survey results fly in the face of the "conventional wisdom on the politics of immigration."

Presidential candidates Newt Gingrich and Rick Perry have both taken criticism for advocating a softer approach to immigration reform. Gingrich said he would "take the heat" from Republicans for deviating from the party's traditional stance. Perry later backed down, characterizing as inappropriate his comment that people who oppose in-state college tuition for illegal immigrant children don't "have a heart."

"The survey showed that likely Republican caucus attendees are supportive of increasing legal immigration and that they are open to several proposals that would expand legal immigration in a way that will spur economic growth," said Jim Kurtenbach, past co-chair of the Republican Party of Iowa and former state representative. "It is critical that we are able to have this important discussion — and that the political discourse and reporting of it are reflective of the openness of Republicans on this set of issues."