The U.S. is facing a nationwide shortage of intravenous bags just as flu cases accelerate, forcing many hospitals to use more time-consuming ways to administer drugs and to weigh a halt on elective procedures and clinical trials.

Some hospital officials said they have only a day or two of supplies and worry whether they would be able to handle an influx of patients as the influenza virus ramps up. Forty-six states are seeing widespread flu activity, according to the Centers for Disease Control and Prevention, putting this...