I used to do a lot of back-to-back long rides most Saturdays and Sundays. That was the bulk of my endurance event training--and I mostly did just fine during those events. While I did ride during the week, those rides were mostly shorter and faster. Regardless, you should ideally get to a point where you can ride 75-80 miles comfortably before doing a century.

But choosing the right century helps as others have said. Make sure there isn't a time limit that you can't easily meet. If the century is likely to be hilly and/or windy; that's fine, but you have to train for those conditions. My first century was hilly. It was challenging, but I did it. Heat is a factor, too. Doing a 100 miles on a 90-degree day with high humidity is tough, even for seasoned people.