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(CNN) – House Majority Leader Eric Cantor is stepping down from his leadership position following his stunning primary defeat.
Cantor threw his support behind the number three Republican in the House, Majority Whip Kevin McCarthy, who has not yet announced whether he will seek the position.
But tea party members would rather not see that happen.
"I don't think the people in the movement want to see anyone who is currently in leadership move into that role," said Jenny Beth Martin, chair of the Tea Party Patriots Citizens Fund.
McCarthy has good relations with House GOP members, and "everyone things he has the inside track," said CNN political commentator and New York Times columnist Ross Douthat.
"There would be an irony here in that Cantor lost in part, we think, because he was perceived as too soft on immigration. From everything we know, McCarthy is much more enthusiastic about a comprehensive immigration proposal than Cantor ever was," Douthat said.
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