Dual Nic Backup server question

The issue at hand is in our office we have a server (windows 2003) that contains all the backups of the production servers. The production servers have different backup types (full or Incremental) and schedules. In the beginning this was all ok as the backups were small, but they have grown as the company has gotten bigger. I have been running into issues where backups are taking longer than expected and I believe I am overloading the NIC on the server. Since the backups are now larger it has become hard to schedule them to run at different times and complete before the next backup starts.

The server has 2 NICs, and I have been searching to see if teaming/Load balancing the NICs would help this situation. I think teaming seems to be what I am looking for as it increases the bandwidth (from what I can gather), but I just want to make sure this is what teaming is used for. Also if this is what teaming is used for are their any draw backs you have seen in a production environment.

If teaming is not the answer could you please give me some other options to look into to correct this issue?

Thanks