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Mr. Romney picked Mr. Ryan to be his running mate because of the House Budget Committee chairman’s expertise on fiscal matters, and groups that want to see a crackdown on illegal immigration said they weren’t worried Mr. Ryan might sway the ticket.

“Although he has co-sponsored amnesties to give illegal aliens a path to citizenship, I can’t find examples of Ryan making speeches, writing op-eds or otherwise publicly advocating for the amnesty,” wrote Roy Beck, executive director of NumbersUSA, in an action alert to its members.

Mr. Beck said Mr. Ryan in recent years has “discarded most of his bad immigration habits from the Bush era.”

Still, NumbersUSA, which graded Mr. Ryan a “C” for his record, asked its members to be on the lookout for any Ryan statements that would help them delve more deeply into his record.

Mr. Ryan’s addition does add some complexity to the ticket with Mr. Romney, who has taken the hardest-line stance of any major-party nominee in history on immigration and used the issue against some of his rivals in the Republican presidential primaries.

Mr. Romney has also backed state immigration laws and courted the endorsements of figures such as Arizona Gov. Jan Brewer and Kansas Secretary of State Kris Kobach, who were instrumental in the push for state enforcement.

The Romney campaign didn’t respond to a request for comment about squaring Mr. Ryan’s stances with Mr. Romney’s — though when asked about differences in general, campaign aides this weekend said Mr. Romney’s positions would take precedence.