The plan agreed to by Mr. Alexander and Senator Patty Murray of Washington, a Democrat, is intended to stabilize health insurance markets under the Affordable Care Act.

As one part of the deal, the subsidies would be funded for two years, a step that would provide at least short-term certainty to insurers. The subsidies, known as cost-sharing reductions, lower out-of-pocket costs for low-income consumers.

The deal between Mr. Alexander, the chairman of the Senate health committee, and Ms. Murray, the panel’s top Democrat, is an important step for lawmakers hoping to shore up insurance markets after Republicans’ failed efforts to repeal the health law.