I tried taking off this hose, and the plastic nub that it was connected to broke off.

What the hell is this thing?
It looks like a vaccum hose; but I don't feel any pressure.
Does it do anything?

Some reason the hose is vinyl, should I change it to a rubber hose?

 

For the sake of fixing it properly I would replace anything I broke.

If you could, take a pic of the parts and post those up so I/ we could see better, also get pic of where that hose leads to so I / we could see what it is attached to.

I took your pic and added some tips... before I reread your question.