If by "sponsors" you mean the political leaders, then yes. They knew they were fudging the books. They explicitly abused the GAO ten year window to make it look like there would be enough money even though the wheels were due to start coming off after seven years.

They also had enough political experience to know getting the (delayed) more unpopular parts (like cuts in payments to doctors accepting Medicare, increases to penalties for people who don't buy insurance, and extra taxes for "Cadillac plans") might be too difficult to get through when the time came. That's why they were delayed.

I suppose I can give them enough benefit of the doubt to say many of them may have believed once the system was in place they could solve the problems by closing the gap with something something.

"Sponsor" is a standard term with a widely accepted meaning when discussing Congress.

https://en.wikipedia.org/wiki/Sponsor_(legislative)

Yes, and it's a word with other meanings as well. That's the one I thought you meant, but I wasn't sure.