You can't overcome a 12-19 start in 20 games. This team is 14-6 in their last 20 games. If they hold on tonight, they'll be 15-6, which is .714 baseball (116 wins over 162 games). They're playing at an extremely high level right now, especially with the injuries they've sustained this year.
Keep playing like this, and keep winning series, and they'll be just fine.
Danny Knobler tweeted earlier today he spoke with a scout who was recently watching the Red Sox. The scout said that if the Sox get healthy, they'll win the AL East.