Currently I have a .NET setup that many workings devs have (VS 2008, SQL SRVR 2008, etc). However, the current client requires webparts to be built on a SharePoint 2003 (it is gov't, so they don't upgrade before doing MASSIVE testing).
I have not developed on SharePoint 2003 and understand that I can only directly create create webparts targeting this platform from VS 2003. Is there any way to create webparts targeted for SharePoint 2003 within VS 2008 (extensions maybe)?
Not with extensions, you would just have to do the old way (but in 2003 Smart Part works, so you have a user control as the container and a easier life). Just reference the 2003 assemblies and test with a custom pre-build event that copies the user controls to the deploy folder (be inetpub's or the /11/TEMPLATES/LAYOUTS) and a custom post-build event that updates the assembly in GAC or BIN folder for your site. That would give you a Ctrl+Shift+B automatic local deploy and Ctrl+Alt+P to attach to any running w3wp processes to debug.