Yes, it is feasible to sell $1 million in BTC (444 BTC at present) in one day. Assuming you're in the U.S., my recommendation is to signup for a Gemini account and read about their daily auctions. They do more than enough volume to fetch you a good price. They're also a highly trusted and very professionally run exchange. I can't recommend them highly enough.

If that doesn't work for you for whatever reason, Bitstamp and Coinbase are both good options. Both have the daily volume to give you a good price on your 444 BTC. Coinbase has pretty strict daily withdrawal limits ($10k per day by default) whereas Bitstamp does not, so I'd try Bitstamp before Coinbase. However, Coinbase can increase those limits if you ask nicely.

Whatever you do, stay away from Bitfinex. They're currently not letting anyone withdraw money.