The missive from Cantor is among the first official indications that an immigration reform measure could come to the House floor this month. The Senate passed its comprehensive bill June 27, and the focus now turns to the House.

But much of how the House moves forward on immigration reform will depend on the feedback that leadership gets from a conference-wide meeting this Wednesday — which Cantor alluded to in his memo.

“I look forward to our special conference on July 10th on how to fix … our broken immigration system,” Cantor wrote.