House Republicans are set for a critical conference-wide meeting on immigration Wednesday, with advocates from across the political spectrum trying to bend their ear on how to handle President Obama’s top domestic priority.

Party leaders scheduled the private session to determine a way forward on an issue that has divided the GOP, pitting senior members of the Beltway establishment in favor of a comprehensive overhaul against conservatives opposed to legislation that they deride as amnesty.

The meeting comes as lines are hardening on the issue following the passage of bipartisan Senate legislation, dimming the prospects for a final bill by the end of the year.