Obama was initially expected to focus only on slowing deportations of potentially millions of undocumented immigrants and altering federal enforcement policies. Now top aides are talking with leaders in big companies like Cisco, Intel and Accenture, hoping to add more changes that would get them on board.

Representatives for high-tech, agriculture and construction interests have put forward a range of fixes, from recapturing unused green cards to tweaking existing work authorization programs.

The outreach is an effort to broaden the political support for Obama’s decision to go it alone on immigration — another sign that suggests the White House fears a backlash in November, particularly among independent voters in battleground Senate races where Republicans are seizing on the issue.