The bullpen is going to get revamped soon, according to GM Mark Shapiro:
"We've spent a lot of time in discussions, not just over the last 24 hours but probably the last three or four days," Shapiro said. "If we feel we can make a move that's going to help this team, we're going to do it. We're considering all moves, from changes in roles to changes in personnel in our bullpen."
The most obvious move to me is to swap Graves with Karsay, moving Steve into an eighth inning role, which would push everyone else down an inning. Rafael Betancourt isn't that far away from returning, so he'll help. There's other interesting options in the minors as well, like Ed Mujica, Andrew Brown, and Rafael Perez.
But the run prevention problems aren't caused entirely by the bullpen; when starters aren't able to go six or seven innings, they make the underbelly of the bullpen pitch with the game on the line. Last season, with a deep and effective bullpen, the Indians could win games when their starters went the "five and fly" route. This season, it's much more problematic if the bullpen has to pitch three or four innings.