I lost my cedula, not my book. So I asked at the counter at one of the shoppings where they do the processing of DNIs, and they told me that they cannot help any foreigners at these desks, the only place foreigners can get services is at Migraciones. So unfortunately you will have to go there. When I asked at the stand in the mall they gave me a little card that has a phone number for them as well -- you can try calling but I suspect you will have to go down there -- Sede Central: 4317-0234, Av Antartida Argentina 1355.
For Renovaciones it is Yrigoyen 952 -- I'm not sure if this would qualify as a renovacion though, for me they said I'd probably have to go to Antartida, but they weren't sure of course!... the phone number for Yrigoyen is 5222-7117, might have less phone congestion so maybe try them first.
Without a DNI you probably wouldn't have much of a problem leaving the country -- they may try and make you pay an overstay fine. But getting back in you would have to pay the reciprocal fee. However if you go to migraciones they will give you a temporary printout of your DNI that is valid for use until the permanent one arrives, so it is probably worth the hassle of going down there just in case. I`d rather have the headache of migraciones now than possibly getting delayed at the airport!