So technically, if the president is ineligible, should any bills he/she signed be returned to: "that House in which it shall have originated, who shall
enter the Objections at large on their Journal, and proceed to reconsider it. If after such Reconsideration two thirds of that House shall agree to pass the Bill, it shall be sent,
together with the Objections, to the other House, by which it shall likewise be reconsidered, and if approved by two thirds of that House, it shall become a Law." - US Constitution
Wow, that'd be a bummer since the Democrats no longer control the house or have a super-majority in the Senate.