They're currently 3-5. However if they win every game they'll be favored in the next three weeks(Redskins, Giants, 49ers), they'll be sitting at 6-5 with a home game against the Panthers.
They'll need to get in as a wildcard, which is more open in the NFC than in the AFC. The Vikings and Panthers are leading that race but aren't very consistent. The Eagles aren't a threat to the Buccaneers because a win by TB against the Redskins would make it very likely the Eagles win the division instead of competing for a wildcard slot. The next closest seeds are the Seahawks and Falcons, both at 4-4 and only a game ahead.
Jameis Winston and Mike Smith are no longer factors. I realize the defense has been awful but in due time the new coordinator should have a positive impact. Fitzpatrick is on fire, and that's even when Desean Jackson quit on the team over Winston. Solidify the defensive side of the ball and this is a Superbowl caliber team.
Is it going to happen? Probably not. Is it likelier than 1-in-1,500? Absolutely. I'd give it 1-in-30.