It's time to look back at another 31-36 team, the 1989 Toronto Blue Jays. There are a lot of similarities with our current Jays team, namely that they were considered a pre-season playoff favorite and they got off to a very slow start. Here is a comparison of winning percentages for the first 3 months of the season (1989 / 2013)
April - .360 / .370
May - .423 / .464
June - .630 / .667 (to date)
The '89 Jays finished 1st in the AL East with a 89-73 record (.549 WP)
The 1989 team was 7 GB of a playoff spot at this point in the season. We are currently 6.5 games back (9.5 in the AL East).
It is interesting to note that in '89 the Jays made it to 36-36 and then proceeded to lose 7 of their next 8 games. They didn't make it to .500 again until they were 50-50 on July 25. They were still at .500 as late as August 14 (59-59), before going 30-13 to finish the season.
Hopefully we can continue to play good baseball and destroy the evil-doers. The Jays don't have to do it all at once, if they gain a couple of games each month, on average, they'll be just fine.