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House Minority Leader John Boehner on Sunday said he's open to talks on changing the U.S. Constitution -- or at least the way it's interpreted -- so that U.S.-born children of illegal immigrants are not automatically U.S. citizens.

"I think it's worth considering," Boehner said.

The top House Republican joined Senate Minority Leader Mitch McConnell in calling for further study of the idea -- something that has been endorsed by prominent Republicans over the past few weeks. Though the call is already running into stiff opposition and faces extremely long odds of ever succeeding, some lawmakers say it would be a way to minimize the incentive for illegal immigration.

"There is a problem. To provide an incentive for illegal immigrants to come here so that their children can be U.S. citizens does, in fact, draw more people to our country," Boehner said on NBC's "Meet the Press." "I do think that it's time for us to secure our borders and enforce the law and allow this conversation about the 14th Amendment to continue."

He continued: "In certain parts of our country, clearly our schools, our hospitals are being overrun by illegal immigrants -- a lot of whom came here just so their children could become U.S. citizens."

Critics of the push to change what is commonly referred to as birthright citizenship say the claims are overblown. Michael Wildes, an immigration lawyer, told FoxNews.com last month that immigrants do not generally come to the United States to have children -- granted, it's a benefit for the child, but the parents would realize no material gain until their children reach 21 years old and can sponsor their parents for legal residency. Wildes dismissed any chance of the move succeeding.

Senate Majority Leader Harry Reid has also ridiculed the idea.

A bill was introduced in April 2009 that called for the law to be changed so "birthright citizenship" as prescribed in the 14th Amendment only applies if one of the child's parents is a U.S. citizen or national, or a legal immigrant -- but that bill has stalled. If lawmakers tried to change the Constitution itself, it would take a two-thirds vote in both chambers of Congress as well as ratification by three-fourths of the states.

However, Sen. Lindsey Graham, R-S.C., broached the topic last month after a federal judge blocked key provisions in Arizona's illegal immigration law. He said birthright citizenship "attracts people here for all the wrong reasons."

Sens. Jon Kyl, R-Ariz., John McCain, R-Ariz., and Jeff Sessions, R-Ala., have all joined Graham in saying the idea should at least be considered.

The United States is one of the few countries that grants citizenship based on birth inside the country.