So I had a quick look at the schedules remaining for all the teams within 2 games of the wildcard spot. I think the number to have a reasonable shot at the division is 11-6 and that would still require quite a bit of luck as the Astros would need to go 8-7 over their remaining 15 games. And with their schedule that would require quite a collapse from them with 6 still remaining with the Royals. But they did just lose a series to Oakland so I guess anything is possible.
Rangers (81-64) - 17 remaining games - 1@Tor, 3@Cle, 3vsBos, 3vsSEA, 3@LAA, 4@SEA
Astros (83-64) - 15 remaining games - 3@KC, 3vsBal, 3vsKC, 3@SEA, 3@AZ
Mariners (81-65) - 16 remaining games - 3vsLAD, 3@Oak, 3@Tex, 3vsHou, 4@Tex
Blue Jays (80-66) - 16 remaining games - 1vsTex, 3vsBos, 3@NYY, 3@TB, 3vsNYY, 3vsTB
If we go 11-6, these are the records the other teams will need to finish ahead of us:
Astros - 9-6 (they have the tiebreaker)
Mariners - 11-5 (12-4 if 2 of our 11 wins come against the Seattle, we currently hold the tiebreaker at 5-1)
Blue Jays - 13-3 (We have the tiebreaker)
So 11-6 to have a decent shot at the division due to the Astros remaining schedule. I think 9-8 would get us the last wildcard spot. The Jays would need to go 11-5 to pass us.
The Astros would have to go something stupid like 5-10 to miss out on the last wildcard. The one thing going against them is that the Mariners and the Blue Jays have the tiebreaker over them.