One bill, with 40 Democratic co-sponsors, would repeal the law’s 2.3 percent tax on medical device manufacturers, a provision that has drawn the ire of members of both parties who say it impedes innovation. 

Another measure, with 20 Democratic co-sponsors, repeals the health law’s Independent Payment Advisory Board, a panel tasked with recommending Medicare cuts if spending rises above a certain target. Some Republicans have labeled it a “death panel,” and it has not been set up yet. Nominees require Senate confirmation, which would set off a fight. 

Repeal of both aspects of the law also passed the House in 2012. 

While the memo does not mention the King v. Burwell case, which could invalidate ObamaCare subsidies for 7.5 million people, the lawmakers will be under pressure to respond to such a ruling. A decision is expected in late June.