He's still president. His mental faculties are relevant....or should be.
If and when the Rs in congress fail to submit a govt funding budget, it will have nothing to do with his ability as a lame duck window. You should really be focusing on the law makers inability to do their job.
Any of the below constitutional assigned duties not being done?
1) Is the Commander-in-Chief of the armed forces of the United States, and of each state’s militia when the nation has need of it
2) Has power to obtain information and opinions from heads of the executive departments
3) May grant pardons and reprieves for crimes against the United States
4) Makes treaties with other countries with the approval of the Senate
5) Appoints ambassadors, federal judges and heads of executive departments – all subject to the approval of the Senate; the President also has power to fill any vacancies that may happen while the Senate is inrecess
6) Must report to Congress from time to time about the state of the union and recommend whatever measures he thinks are necessary
7) May call members of Congress together on extraordinary occasions, as well as adjourn their meetings when they cannot agree on their own about when to do this
8) Receives foreign ambassadors and other public officials
9) Is responsible for enforcing the nation’s laws
10) Issues commissions to all officers of the United States
He tried to get laws passed to work on the immigration bill, but the Republicans in Congress squashed that re #9