Good initial drafts, but I think I need to be more clear:
Treat "Walk a Mile" as the 'company name.' The emphasis for this logo needs to be on the Walk a Mile campaign, not on Third Street Clinic (a note on how this will be used: Third Street Clinic will use our existing logo along with the Walk a Mile logo. This logo is merely to brand a short- to medium-term campaign, not replace our existing brand.)
Revision to this comment: The more logos I'm seeing, the more I realize it's possible to have a successful logo without "Walk a Mile" in the final product. As we promote the organization and this campaign, we will be speaking about our clients and their challenges. We'll share stories. And then we'll end by encouraging everyone to "Walk a Mile with Third Street Clinic."
Whether you use the name of the campaign, or simply imply it with imagery and Third Street Clinic's name, the winning logo will be the one that best captures "Walk a Mile with Third Street Clinic" in visual form.
Thanks again for submitting! I'm going to offer as much feedback and reaction as possible to give the most for designers.