A coalition of conservative groups Thursday urged congressional leaders to suspend or repeal Obamacare's taxes targeting insurers and medical device manufacturers.

The health insurance tax, which was suspended this year after Congress learned unsubsidized premiums were set to increase by double digits, would lower premiums for exchange enrollees by between 3 and 5 percent. The other tax, a 2.3 percent tax on medical devices set to go into effect in 2018, has long been targeted by members of both parties for repeal or delay.

If it goes into effect in 2018, then it would result in 25,000 job losses by 2021 and increase taxes by $30 billion in a decade, according to the conservative American Action Forum.

"Ideally, both the health insurance tax and medical device tax should be repealed permanently, as should all one trillion dollars of Obamacare taxes," the group wrote in a letter. "However, given the recent collapse of healthcare reform legislation, lawmakers should act to delay these two taxes so they do not hit taxpayers in 2018."

The letter was signed by a coalition of conservative groups, including Americans for Tax Reform, Center for Individual Freedom and FreedomWorks.

It comes weeks after Republicans failed to pass a healthcare bill to repeal and replace portions of Obamacare.

Now, some members of the Senate are vowing to work together to stabilize the exchanges when they return from recess. The exchanges have suffered as they have faced federal uncertainty and as insurers have lamented about massive losses. Premium rates are expected to increase for people who do not receive federal subsidies, and some counties are facing the prospect of having no insurer to buy coverage from next year.