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Romney's Arizona campaign recently lost one of its top border-hawk surrogates. Sheriff Paul Babeu, a co-chairman of Romney's Arizona campaign, left his position after a former boyfriend accused Babeu of threatening him with deportation if he publicly discussed their relationship.

The accusation publicly outed Babeu and compromised him as a spokesman for Romney with just one week to go before the primary.

Romney has successfully positioned himself as a more conservative GOP candidate on immigration than Perry or Newt Gingrich, but Santorum hasn't shown weakness on the issue among conservatives.