Almost looks like common chickweed. Do you have a better closeup of the flowers?

OK, did some further research and I am pretty sure it is thyme-leafed speedwell (Veronica serpyllifolia). So, you were right in your suspicion that this is a member of the veronica genus.

Check out the link below as well as the wikipedia entry: http://en.wikipedia.org/wiki/Veronica_serpyllifolia

Here is a link that might be useful: Thyme-Leafed Speedwell

Veronica serpyllifolia

thyme-leaved speedwell

Don't know what's its called but once you have it you will always have it! heat and hot weather will do it in, but it WILL be back!

r u sure its not a persulane? They r sold at nurseries,& called a weed.I call them zombie weeds,cause they just wont die!!!! If you dig them up,roots and all & leave ANY part(leaf,stem,root) on the ground,it will re-root itself & if u dont seal them in a bag get them far,far away asap,they will project their demon seed all over.They r the devil