The 1993 Giants went 103-59 and missed the playoffs, but in those days, only the 4 division winners made the playoffs. In the Wild Card era (after 1993), the best record to miss the playoffs was the 1996 Reds (96-67). After that, three 93-win teams missed the playoffs (2005 Indians, 2003 Mariners, 2002 Red Sox). Braves will make the playoffs, and will win the division unless the Nats go at least 5-2, and probably need to go 6-1 in their remaining 7 head to head games. Not likely.
FWIW, Fangraphs currently projects the following win totals for NL teams:
Dodgers: 104
Braves: 96
Nats: 91
Cards: 88
Cubs: 88
Mets: 84
Phillies 83
Brewers: 83
If the season played out that way, Cards and Cubs would have a one game playoff to determine the division winner and the 2nd WC. The playoff bracket would be:
WC: Cards v. Cubs loser @ Washington
NLDS: WC Winner v. Dodgers and Cards v. Cubs winner v. Braves.
Pretty compelling.