A Department of Veterans Affairs hospital project near Denver came to a standstill this week after federal judges ruled the VA was in breach of contract, hundreds of millions of dollars over budget and devoid of a plan to adequately fund the facility.

The billion-dollar project is one of four large VA construction plans that in recent years have faced cost and schedule overruns, as well as scrutiny by legislators and government auditors. The agency is moving to upgrade its facilities amid the growing number of veterans returning...