I don't know. How many is "a lot"? Will we lose some, absolutely. The guys in middle relief aren't good enough to start a game or finish it. Middle relief pitching is generally where teams lose games.
I understand looking at the 40-man doesn't get me thrilled when they'll have to go to the bullpen after the 6th up a run or two. But there are servicable options:
Tejeda
Bale
Gobble - as LOOGY
Peralta - not sure what happened last hopefully he can regain his confidence.
Farns - even though I don't like him he is still a power arm.
Here is a list from RC, don't know if its up to date past the 1st:
Relievers
Luis Ayala (31) - Type B, not offered arb
Joe Beimel (32) - Type B, not offered arb
Joe Borowski (38)
Shawn Chacon (31)
Chad Cordero (27)
Juan Cruz (30) - Type A, offered arb
Elmer Dessens (37)
Brendan Donnelly (37)
Scott Elarton (33)
Randy Flores (33)
Keith Foulke (35)
Eric Gagne (33) - Type B, not offered arb
Tom Gordon (41)
Eddie Guardado (38)
Jason Isringhausen (36) - Type B, not offered arb
Tyler Johnson (27)
Jon Lieber (39)
Aquilino Lopez (34)
Will Ohman (31)
Al Reyes (38)
Dennys Reyes (32) - Type B, offered arb
Ricardo Rincon (39)
Rudy Seanez (40) - Type B, not offered arb
Ken Takahashi (41)
Julian Tavarez (36)
Mike Timlin (43)
Ron Villone (39)
Kip Wells (32)
Matt Wise (33)
Jamey Wright (34)
Who else do you want?