WASHINGTON—Support grew in the House for an effort to force a vote on several immigration proposals, sparking some conservatives to consider using a coming vote on the farm bill as leverage to try to block them.

GOP Reps. John Katko of New York and David Trott of Michigan on Wednesday joined a push from 18 other centrist Republicans to force a House floor vote on a series of immigration bills, including ones with a path to citizenship for young undocumented immigrants known as Dreamers. That left the GOP centrists just five...