Not working for me, and I've tried at least three possible solutions, " ",+,_,and %20 for the space.  None work.

Here's the situation, maybe you misunderstand the problem and the results.

I put this command (at the end of the template as any earlier and it puts and annoying blank line in the message) in my new message template for a listserver address:

%FROM="Vendor Input Coordinator"

And it's delivered with this:

From:    VendorInputCoordinator <VendorInputCoordinator>
To:       <>
Date:    Wednesday, April 9, 2008, 3:34:23 PM
Subject: test8
Files:   <none>

This carries to a reply message as well.

It should have spaces in the name  and say "Vendor Input Coordinator" a minor problem, but important to me.

Your problem is yoru're trying to use a From header without an address, according to RFC2822 that's illegal, so TB interprets the contents of the From header as an address.
Addresses aren't allowed to have spaces in them, so TB ignores the spaces.

Try something like this:
%From='"Vendor Input Coordinator" <your address>'

The empty line issue can be explained (and remedied) easily.
Your macro is located in the text body of your template. However, it doesn't result in any text in the body (only in the header) so it results in an empty line in the body. As far as the text is concerned its is an empty line, isn't it?
In order to skip the empty line, you have to tell TB to skip the line feed after the macro. That can be done with the %- macro (you'll find that in the help file too)

So your From macro will result in this:
%From='"Vendor Input Coordinator" <your address>'%-