Two taxes on the health insurance and device industries will disappear if Obamacare is ruled unconstitutional, but trade groups that oppose those provisions say the general law can remain intact.

The health insurance tax and medical device tax, which are both delayed until 2020, are components of Affordable Care Act. The health insurance tax hits insurers on health policy premiums and is roughly based on their market share. The device tax requires a 2.3 percent excise tax on medical device sales.

The entire law is in the hands of a federal appeals court as it mulls whether a federal judge...