Yes I believe she is an Obama supporter.
I remember when Jay was not like this, but a friend told me he changed after his mother died. That is when he began to become liberal.
As for Cruz I think he held up well with being tossed hardball questions like his father which has nothing to do with Obamacare or his politics. I do not recall Leno asking Obama about his father. I am glad Cruz did this because it will expose him to more wide audience.
When Sarah was on Jay's show, he asked her if her dad still gave her advice, like political advice. Sarah replied, "Not political, but he advises me about which ammo to use!"
The audience loved it...and Jay even got a kick out of her answer, too.