The insurance industry's biggest lobbying group on Thursday sent a wish list to the Republican-led Senate about the types of changes they would like to see in a bill to repeal and replace Obamacare, including a recommendation to control health spending.

The recommendations from America's Health Insurance Plans had been requested by Senate Finance Committee Chairman Orrin Hatch, R-Utah. The health insurance industry has covered millions of people under Obamacare, by providing plans to people that are paid for partly by the federal government. Insurers have until June 21, or sooner in some states, to decide if they will keep offering those plans. With Republicans' vow to repeal and replace Obamacare, and with big losses incurred over a few years, some insurers have already decided not to participate.

In its letter to Hatch, the group noted that "the individual market clearly faces immediate and significant challenges, especially for the 2018 plan year." The group attributed some of the problems to both the structural issues with the law as well as to the uncertainties insurers face about the future of the law. They do not know, for instance, whether the federal government will continue paying insurers cost-sharing reduction subsidies or whether the administration will enforce the individual mandate that requires people to have insurance or pay a penalty.

The group asked for those items to be made certain or for Congress to find another way to incentivize people to get insurance. It also asked for Congress to create a reinsurance program, to repeal or again suspend the health insurance tax, to increase tax subsidies for younger customers, and to hold off on major changes until after 2019.

The group noted that most Medicaid policies are handled by private insurers and recommended that the insurance program for low-income Americans be adequately funded and give states more flexibility on how to run it, and similarly for any funding of high-risk pools to be high enough so they are sustainable.