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I just got off the phone with Discover. They told me that "select users" were able to have one login for both accounts, but I was not one of them. They said that they are working on changing the website so that I could log on to both accounts at the same time, but I should set up a different account for now. He told me I would be able to combine both accounts once they let everybody create a single login.
I originally signed into my credit card login when I set up the checking account, but I got an error message at the end and I had to finish setting up the account over the phone. Maybe that's why it didn't combine the accounts on the website.
Sorry to revive an old thread, but I thought it might be helpful for people looking for help now. I made a new checking account the other day and at the end it made me sign up for a new username and password even though it previously asked if I had a Discover login, which I did since I have a credit card through them. When I logged in with each username it just took me to the respective account. Then I went to login today, funnily enough to contact support about connecting my accounts, and it prompted me to do just that. It asked for each username and password and voila! Hope this helps.