WASHINGTON — The White House is backing a health care proposal that would make it easier for insurance companies to avoid complying with consumer protection standards, siding with some of the most conservative senators, though Senate Republican leaders remain leery of the idea.

The proposal, advanced by Senator Ted Cruz, Republican of Texas, is one of many being analyzed by the Congressional Budget Office as Senate Republicans try to muster votes for their bill to repeal major provisions of the Affordable Care Act. It could help bring balking conservatives, such as Rand Paul of Kentucky and Ben Sasse of Nebraska, aboard, but it may do little to ease the concerns of moderates like Susan Collins of Maine and Lisa Murkowski of Alaska.

Under the proposal, insurers could sell almost any kind of health plan they wanted as long as they also offered at least one plan that complied with federal mandates like those in the Affordable Care Act, including coverage for maternity care and mental health services.

Senator Mike Lee, Republican of Utah, and Marc Short, President Trump’s director of legislative affairs, said over the weekend that they supported the proposal. On Wednesday, Representative Mark Meadows, Republican of North Carolina and the leader of the conservative House Freedom Caucus, said on Twitter that he would back the Senate’s health bill if it included the Cruz plan.