The only reason to "sell" right now is to open up roster spots and/or playing time, as we're not going to get anything much at all for anyone we don't want next year. Peavy needs to go, not because we're going to get any kind of return but because we need the roster spot.
Selling usually means trading good veterans for young talent. We don't really have any good veterans that we don't want next year too. So there's no need to sell in the usual sense. Clear out some guys who won't be here next year? Sure, but don't expect anything back for them. And don't do it until you've got someone ready to take over for them.
We've got a couple good candidates for Peavy's spot, so we should move him. No one else has a replacement yet (I think we'd be just as good overall offense + defense with Vazquez catching as Pierzynski, but the team clearly does not agree, so it's not gonna happen yet.) If we keep losing for another couple weeks, then Drew is probably next up on the dumping block, once we get either Victorino or Middlebrooks back. We're not going to get anything good for him either though.
People want to "sell" Lester, but we would need to bring back more value than the high pick we'll get for offering him the qualifying offer to even consider it. That's probably more than any other team would offer, since the Red Sox value those high picks quite a bit. We should be trying to get him to sign an extension anyway, we'll need him next year or we'll probably have to sign someone to a worse contract to replace him.
By the 4th of July, we could be as close to first as maybe 5 games, or as far out as maybe 10 or 11 games. This is a big week. If we go 5-2, we should still be in contention for the division in early July. If we go 2-5, we'd be 10 games under .500 with another week off the schedule. Anything in between and we're not quite done but running out of time to put up a fight.
Might be time to bring up Markus Lynn Betts, who is now over 100 PAs in AAA and hitting .330/.422/.455 with 7 stolen bases, reaching base in every game. You could replace Herrera with Betts and see if he can give us a lift. But that depends if the team thinks he's ready for it yet.