NAD83 is more an ellipsoid description than a projection, and from the below, basemap probably supports it:

basemap/packages/basemap/src/mpl_toolkits/basemap/__init__.py

Lines 315 to 318 in 461b402

    
            ellps            string describing ellipsoid ('GRS80' or 'WGS84', 
        
                             for example). If both rsphere and ellps are given, 
        
                             rsphere is ignored. Default None. See pyproj.pj_ellps 
        
                             for allowed values.

UTM zone is a collection of specialized Transverse Mercator projections, as noted in the UTM example:

basemap/examples/utmtest.py

Lines 15 to 19 in 461b402

    
           # mimic this with Basemap (WGS84 ellipsoid, with scaling factor of 0.9996 at 
        
           # central meridian).  latitude bounds are given for the MGRS band N, which covers Florida. 
        
           m = Basemap(projection='tmerc',lon_0=lon_0,lat_0=lat_0, 
        
                       k_0=0.9996,rsphere=(6378137.00,6356752.314245179), 
        
                       llcrnrlon=lon_0-3,llcrnrlat=24,urcrnrlon=lon_0+3.,urcrnrlat=32,resolution='i')

so this should be a matter of adding a lookup table to turn UTM zone into Transverse Mercator parameters (or perhaps UTM is designed such that this can be a helper function with multiplication rather than a lookup table).

Since it sounds like you have experience with UTM, perhaps you would be willing to expand that example to include a function to turn UTM zone into lon_0?

	ellps string describing ellipsoid ('GRS80' or 'WGS84',
	for example). If both rsphere and ellps are given,
	rsphere is ignored. Default None. See pyproj.pj_ellps
	for allowed values.

	# mimic this with Basemap (WGS84 ellipsoid, with scaling factor of 0.9996 at
	# central meridian). latitude bounds are given for the MGRS band N, which covers Florida.
	m = Basemap(projection='tmerc',lon_0=lon_0,lat_0=lat_0,
	k_0=0.9996,rsphere=(6378137.00,6356752.314245179),
	llcrnrlon=lon_0-3,llcrnrlat=24,urcrnrlon=lon_0+3.,urcrnrlat=32,resolution='i')

about projection #605

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