Short-term health plans with a history of consumer complaints will get a larger role in the U.S. insurance market under a Trump administration plan to expand alternatives to Obamacare.

The temporary plans, which were originally intended for people between jobs, are allowed to offer coverage that’s far skimpier than what the Affordable Care Act requires. The administration has promoted them as a cheaper alternative to Obamacare for individuals who have seen their premiums climb or lost access to doctors. The...