House Democrats are pushing to make it harder, if not impossible, to allow offshore drilling on the east and west coasts of the U.S. with several measures approved June 20.

The chamber adopted a number of amendments to the fiscal 2020 “minibus” spending bill (H.R. 3055) that would exempt large parts of the Outer Continental Shelf from drilling, an effort that has attracted bipartisan support from coastal-state lawmakers.

The House is expected to vote on final passage of the spending package June 25, but the pro-Democratic provisions face tough odds in conference with upcoming Senate appropriations...