Kevin Appleby, director of migration and refugee policy for the U.S. Conference of Catholic Bishops, was among those attending the meeting.
"The key to victory is that all interested parties must work for the entire bill, not just their piece," Appleby said. "We all live or die together."
House Republicans are largely dismissive of advice being handed down from on high, saying they are more interested in hearing what their constituents have to say.
"I pay more attention to what I hear in my district than what I do from various groups," said Rep. Charles Boustany, R-La.
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