To reach the playoffs, the Padres would have to fight their way to a spot currently occupied by the Brewers or the Fish who have identical records, 57-49. The Brewers and Fish both have 56 games left.
If they go .500 the rest of the way, they'll finish with records of 85-77.
The Padres are currently 52-54. To tie our hypothetical Brewers and Fish record, they'd have to go 33-23. That's a .589 win percentage. To win outright they'd have to have a .607 win percentage
Currently, only Baltimore, Tampa Bay, and Atlanta have won at a .589 win percentage or better this year.
I don't think San Diego can reasonably expect to play at a .600 win rate the rest of the year. So they'll need other teams to play poorly. The Brewers have the second easiest schedule the rest of the way so they could be hard to catch. Then there's the fact that the Phillies are only 0.5 out in the wild card and are better than either the Brewers or Marlins. There's also the Cubs fighting ahead of you who have almost as good a run differential.
I know why San Diego wants to go for it. It's tempting. But they have to play out of their minds and have teams ahead of them face plant. I don't like their odds.