Did you take the Y-DNA test or the autosomal test (AncestryDNA)?
The Y-67 test at FTDNA is needed for such a situation. It will pair down the number of false matches. You will likely have matches with several people in the correct family. Singletons may just be outliers, depending on the size of the project.
The next step is to go to the surname sites at FTDNA and find your matches' groups from their kit numbers and compare your values (haplotype) to the group modals. (This is the most common value at each marker and a good proxy for the progenitor's haplotype). This will eliminate recent mutations and may give you closer matches. I would view 63/67 or better matches as promising.
However, even a very close match will only pare down the number of possible surnames, since there may be thousands of people who closely match the family progenitor's haplotype. The participants may know little about the family genealogy, so you may need to search the surname boards here and at Genforum to find researchers.
Autosomal tests (23andMe, AncestryDNA and Family Finder) are used to try to find close relatives who might have information. It is a good idea to test (or transfer at FTDNA) at all 3 firms to maximize the chances of matches. I would not bother contacting anyone more remote than 3rd cousins. Even that might be too remote to provide any useful information in this situation.
There is a lot of serendipity involved. I was helping someone with a similar problem. He tested at 23andMe and Ancestry without getting useful matches. He then tested at FTDNA and found two second cousins once removed, even though its database was smaller. They were sisters of the prime suspect, obtained from a tree at Rootsweb.
The test of the future is full Y-genome sequencing. The databases are now very small. However, as prices drop, they will grow. Full Genomes Corporation has the gold standard test, but FTDNA has a good test (Big Y).
Richard Hill's web site has more information. It's a commercial site, so I cannot post the link. However, searching with his name and DNA brought up a number of hits.