You may try to focus on a few major platforms rather than individual distributions. What I mean by that is to build on what I call the "foundational distros" (Debian and RedHat) and hope for the best on the others.
Most likely, Debian binaries (that are statically linked) will run just fine on Ubuntu and Mint and other Debian derived distributions. RedHat binaries will probably run on Centos, Scientific Linux and SuSE Linux. If you care about less popular distros (Say you have a lot of customers running some uncommon Linux), and neither your Debian or RedHat executable works on them or can be made to work somehow, then setup a VM of that distro and build one executable specifically for that flavor.
I've taken this approach in the past and it has worked well.