WASHINGTON — Veterans who have trouble getting timely mental health care from Veterans Affairs hospitals and clinics should also have access to thousands of health care providers who care for military personnel and their families, says the Republican chairman of the House Committee on Veterans Affairs.

The proposal by Representative Jeff Miller, Republican of Florida, borrows from the playbook of Republican Mitt Romney, who raised the idea of tapping into the military’s Tricare network of doctors during the course of the presidential campaign.