I think the key is to help empower small, veteran owned businesses and service disabled veteran owned businesses to help better market themselves and grow their businesses. Veterans are notorious for helping other veterans out. You help a business grow that is owned by a veteran, it's likely said business, when times are better, will turn around and help out in their community including putting forth programs and funds to help homeless veterans. While this isn't a cure for the problem, it certainly another way that we, as Americans and also humans, can help.
For a good idea of the amount of veteran owned businesses out there, take a look at the VA's veteran owned business website at VetBiz.gov - http://www.VetBiz.gov as well as VeteranOwnedBusiness.com - http://www.VeteranOwnedbusiness.com. Both have very comprehensive lists of businesses in the United States owned by veterans, active duty military, reservists and service disabled veterans.