I've just been rereading When The Cheering Stopped, about President Wilson's breakdown in 1919. An incredible tale, but it struck me that in some ways America was lucky. Had the stroke come during WW1, or in the run up to American entry, rather than in the aftermath, the problems could have been hugely greater.
So WI Wilson collapses in February 1917? Seems to me there are about four options.
1) Resignation. The logical choice, except that Wilson and those around him are contemptuous of the Vice President, while Mrs Wilson fears that giving up the Presidency might leave her husband without the will to live.
2) Press on regardless. Go on as OTL, though with Wilson's war message having to be read to Congress by someone else. But in Wilson's present condition, the strains of tryng to lead the country in war are likely to kill him in short order, so this is just a more drastic form of (1).
3) Play for time. Though all believe war to be imminent, it doesn't necessarily have to be declared in April. Dr Grayson and the First Lady may try to stall, in the hope that two or three months hence, Wilson will be sufficiently recovered to take the helm again, even for war. In hindsight, almost certainly wishful thinking, but that might not become obvious for some time.
4) Constitutional coup. Starts off as (3), but at some point Vice President Marshall is prevailed upon to claim Presidential powers, on the ground of Wilson's inability. But if Marshall's record in 1919/20 is anything to go by, he would be very resistant to any such suggestion, fearing that the doubtful legality of such an act would create as many problems as it solved.
For my money, option (3) sounds about the likeliest, but nothing is guaranteed. Any thoughts on how the situation might develop?