We are using a non-free solution, the CLC Genomic Workbench. This software has MANY capabilities. In the role you are asking about, it would easily assemble millions and millions of short reads (given enough RAM, and, of course, a 64bit system to use it). You can easily put in data from different taxa, specify different criteria for the assembly, or alternatively, use a reference genome to assemble your data on, so as to potentially get a less messy result (less influenced by sequence divergence, paralogy...).
This software could be somewhat pricey for a small lab, but in the context of a group of research, I have found that it was many times worth it's price just in time saved on student projects.
The software also has A LOT of features for biologists working with sequences. Not only assembling NGS data.
DISCLAIMER (just in case...): I am IN NO WAY connected to this company. I just happen to be a happy user :)