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 maternity care, emergency services and mental health coverage.

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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 House’s hard-line Freedom Caucus, announced that he would back the Senate’s health bill if the Cruz plan were included.

The proposal would guarantee access to “at least one Obamacare-compliant plan,” Mr. Lee said on CBS’s “Face the Nation.” And, he said, consumers would also have less expensive options.

Mr. Cruz says his plan would fix a problem he sees in the Affordable Care Act. “Obamacare’s insurance mandates caused premiums to skyrocket,” he said in a summary given to Republican senators. One of those mandates requires insurers to cover 10 types of benefits, including drug abuse treatment, prescription drugs and pediatric care.

Mr. Short said on Fox News on Sunday, “We support Senator Cruz and Senator Lee’s efforts.”

“The mandates the federal government puts on are so ridiculous that men are forced to carry coverage for mammograms, women are forced to carry coverage for prostate issues — it’s absurd,” Mr. Short said. “And the American people know this. We’re going to get rid of many of those regulations and mandates to lower cost.”

But insurance experts worry that the proposal would bifurcate the insurance market, sending the healthy to cheaper, less comprehensive insurance and the sick to plans that comply with all the federal mandates. That could make those comprehensive plans prohibitively expensive, which would raise the issue of pre-existing conditions that dogged House Republicans as they struggled to pass their version of the health bill in May.

“People who have higher health care needs and need more comprehensive coverage would choose A.C.A.-compliant plans,” said Cori E. Uccello, a senior fellow at the American Academy of Actuaries. “People who are healthy now would tend to choose noncompliant plans with really basic benefits. People who want or need more comprehensive coverage could find it out of their reach, because it might become unaffordable.”

Some Senate Republicans share that concern. The proposal, they say, would undermine their contention that they are preserving protections for people with pre-existing conditions.

“I believe it would lead to adverse selection in the marketplace,” Ms. Collins said. “It would also vitiate the important consumer protection of having a prohibition against annual and lifetime caps” on benefits.

The fate of the repeal bill is unclear as senators face pressure from constituents during this week’s Fourth of July recess. Thousands of protesters showed up on Wednesday at more than two dozen events in 17 states, urging senators to reject the legislation.

Senators in both parties have questioned whether Mr. Cruz’s proposal can survive under strict budget rules being used to advance the repeal bill. The rules preclude a filibuster and allow passage with a simple majority vote, but generally require that provisions of the bill affect federal spending or revenue.

The Club for Growth, an influential conservative organization, prodded lawmakers to pass a repeal bill with Mr. Cruz’s proposal.

“After almost a decade of promising to repeal Obamacare, it’s time for Republican senators to put their money where their mouths are and get it done,” said David McIntosh, the group’s president. “At a bare minimum, Congress should not stand in the way of allowing Americans who want to opt out of Obamacare to do so.”

The Senate bill, drafted mainly by the majority leader, Mitch McConnell of Kentucky, would make it easier for states to obtain waivers from requirements in the Affordable Care Act.

In a letter to Senate leaders, the American Academy of Actuaries said the waivers would let insurers offer less generous plans covering fewer medical needs. While such plans might have lower premiums, it said, consumers could face higher out-of-pocket costs, including “much higher deductibles,” when they receive care.

Indeed, the group said, insurers might focus on selling less comprehensive plans so they could offer lower premiums and “avoid attracting unhealthy enrollees into more generous coverage.”

The Affordable Care Act limits out-of-pocket spending, but only spending for covered services counts toward the limits, the academy said. Letting insurers reduce the scope of benefits would thus erode protections for people with pre-existing conditions.