Democrats said the Republican bill would be dead on arrival in the Senate, even if it passed the House.
Many members of the US Congress are older than President Biden. Are they still suitable?
McConnell, who has served in the Senate since 1985, fell and suffered a concussion and a broken rib in early March and missed six weeks of Senate action.
Currently serving his seventh term, which runs through 2026, McConnell is the third US senator to be hospitalized in recent weeks.