After 113 games, the Jays are 57-56 and 6 and 1/2 games out of the wild card berth, currently held by Seattle, with Detroit and the Yankees a game back and the Twins 6 back. The Jays have a run differential of +39. Shall we go back over the last 50 years at some clubs that have made a late rush?
The '64 Cardinals
On August 12, 1964 after 113 games, the Cardinals stood at 60-53, with a run differential of +9. They were 8.5 games behind the Phillies, 4.5 behind the Giants, 2 behind the Reds and 1 behind the Pirates. They went 33-16 from there on out to nip the Reds and Phillies at the wire. The popular view is that Lou Brock's arrival triggered the Cardinal run, and it is true that he did hit well, but the Cardinal offence was not particularly hot down the stretch. The club hit about as well as they did the remainder of the season, which was not particularly well given the nature of Sportsman's Park. Rather, it was the pitching of Bob Gibson particularly, but also Curt Simmons, Ray Sadecki and young Mike Cuellar that was the key to their run. The Cardinals were also a little lucky, as the Reds were probably a slightly better club.
The '78 Yankees
On August 10, 1978 after 113 games, the Yankees stood at 64-49 with a run differential of +65. They were 7.5 games behind the Red Sox, and went 36-14 to catch the Sox (who actually went 28-23 down the stretch). It is not really a good comparison, because the Yanks were pretty clearly a better ball club than the Jays are this year.
The '04 Astros
On August 11, 2004 after 113 games, the Astros stood at 56-57 with a run differential of +37. They stood 6 games behind the Cubs for the Wild Card berth, and 4 behind the Padres, 3 behind the Giants and 2.5 behind the Phils. That is a pretty close comparison with the Jays' current situation. They went 36-13 the remainder of the way to capture the wild card berth. Carlos Beltran, who had been acquired in June from the Royals played a key role, but the Astros had been above .500 when he arrived and floundered for seven weeks before catching fire, with the offence playing a leading role.
So what about the 07 Jays?
Yes, they can. That of course does not mean that they will. What they have going for them is four starting pitchers in Halladay, Marcum, Burnett and McGowan, who if healthy can give them at least 6 good innings the great majority of the time, with sufficient offensive and bullpen support so that a 35-14 finish is possible. Unlikely, but possible. If they get to 92 wins, they've got a shot. Like the Cardinals of 64, they will need some luck though.