This is the first definition given in the Oxford Advanced Learners Dictionary:
1 used in negative sentences and questions, or sentences with if to mean ‘at any time’
Nothing ever happens here.
Don't you ever get tired?
If you're ever in Miami, come and see us.
‘Have you ever thought of changing your job?’ ‘No, never/No I haven't.’
‘Have you ever been to Rome?’ ‘Yes, I have, actually. Not long ago.’
She hardly ever(= almost never) goes out.
We see them very seldom, if ever.
(informal) I'll never ever do that again!
And this is the second
2 used for emphasis when you are comparing things
It was raining harder than ever.
It's my best ever score.
The definition ‘at any time’ in the first definition continues in the second, which is what is in play here—Obama is drawing a comparison (‘more’) between how hard Americans work today and how hard they worked in the past:
So: “Americans are working more than [they worked] at any time [i.e., any time in the past] just to get by.”