ORANGE, Va. — Alice Jacobs, 90, once owned a factory and horses. She has raised four children and buried two husbands.

But years in an assisted living center drained her savings, and now she relies on Medicaid to pay for her care at Dogwood Village, a nonprofit, county-owned nursing home here.

“You think you’ve got enough money to last all your life, and here I am,” Ms. Jacobs said.

Medicaid pays for most of the 1.4 million people in nursing homes, like Ms. Jacobs. It covers 20 percent of all Americans and 40 percent of poor adults.

On Thursday, Senate Republicans joined their House colleagues in proposing steep cuts to Medicaid, part of the effort to repeal the Affordable Care Act. Conservatives hope to roll back what they see as an expanding and costly entitlement. But little has been said about what would happen to older Americans in nursing homes if the cuts took effect.