Is it possible to use the same ssh private/public key pair on 2 machines to access a git repository?

Yes I think you can.

I have something similar. Two machines, one Intel (desktop) the other one Sparc. I can log into both machines and access the same CVS server (another machine) using SSH access with the same key pair which was generated on the Intel machine.

Make sure when you copy across your private key that you set both the permissions of the .ssh directory correctly (0700) and your home directory cannot be group or world writable. The id_rsa should only have user read access (0400)

Yes, that's perfectly legitimate. ssh keys don't care where they were generated, and it's fine to have them on multiple machines at once.

Try giving the ssh client the "-v" or "-vv" option (for verbose output) and check the server's ssh log to debug the problem.