I understand the process of obtaining btc but I might not have read in enough. I noticed blockchain.info doesn't get any support, and that's where btc comes from, right?
You might be confusing the
blockchain which is a distributed database which holds a record of every bitcoin transaction and is sort of where btc comes from and the website
blockchain.info which amongst over things displays information about the blockchain database.
Is it possible everyone could wake up one morning and blockchain.info be gone? What would happen to btc?
Yes. Nothing, unless you have a wallet host at blockchain.info in which case a wallet backup can be imported into another client and be up and running again fairly quickly.