The nation's largest association of health insurance companies said Wednesday that it opposes Sen. Ted Cruz's effort to allow insurers to sell plans that don't comply with Obamacare.

America's Health Insurance Plans, the top insurance industry lobbying group, said a proposal from the Texas Republican would further destabilize the individual market and increase costs for sick people. The Blue Cross Blue Shield Association, which represents insurers that are heavily involved in the exchanges, also wrote Wednesday saying that the amendment would "undermine pre-existing condition protections, increase premiums and destabilize the market."

The opposition comes at a critical point for the proposal, which is being evaluated by the Congressional Budget Office. Cruz and other conservatives have signaled that inclusion of the proposal is vital if they are going to support the Senate's healthcare bill, which could be voted on next week.

The proposal would allow insurers to sell plans that don't comply with Obamacare's insurer mandates, as long as some plans do meet those mandates. Insurer mandates include protections for people with pre-existing conditions.

Cruz has said his plan is a good way to lower premiums, which is a main goal of conservatives with the healthcare bill that only partially repeals Obamacare.

Cruz told reporters Wednesday that he wasn't surprised that insurers opposed his proposal.

"The insurance companies have made billions of dollars under Obamacare," he said. "Their focus appears to be on maximizing their own subsidies at the expense of consumer choice."

But AHIP and the Blue Cross Blue Shield Association said setting up two insurer markets — one for Obamacare-compliant plans and one for non-compliant plans — could lead to greater instability in the individual market used by people without employer coverage.

The groups argue that only sick people would pay for the more comprehensive Obamacare plans, and healthy people would likely buy the cheaper non-Obamacare plans. That would cause costs to spiral out of control on the Obamacare plan market, the groups say.

"Stable and well-functioning insurance markets require broad-based enrollment and a stable regulatory environment that facilitates fair competition and a level playing field," AHIP said.

The Cruz proposal, however, has received major support from the conservative House Freedom Caucus and outside conservative groups. While GOP leadership said the proposal is still in the mix to make it into the final version of the bill, the result of the CBO score will play a major factor.

Kimberly Leonard contributed to this report, which has been updated