That's a lot of parcels to process! Are you using a personal geodatabase? I ask because you are limited to 2GB of storage in a personal geodatabase and this could be a potential stopping point for you. If you are, switch to a file geodatabase and see if that works. You could try shapefile as well. Also, have you checked your environment settings for "Current" and "Scratch" workspaces? Your computer may be limited in the default temp location. Try changing this to another location and see if you still get the same message.
More than likely, there are just too many parcels to process at once. What you may want to do is use a "Model Iterator" and see if that helps. In Modelbuilder, you can go to "Insert," then "Iterators" to see the options. Do you have a field that designates the County, District, or State (with this many parcels I'd say you have multiple states)? If you have, for example, the State FIPS code in a field, then you may want to try the "Iterate Feature Selection" iterator. This will look at the field you specify (in this case the State ID) and conduct a model run (or iteration) for each unique value in that field. So, if you have parcels for three different States, it will run the model on the first state, then the second, then the third. I attached an example of a this. You will have to copy the selected features to a new feature class for each State, then merge them together to get back to one all-encompassing dataset. You can do this by inserting the "Collect Values" tool (Insert, Model Only Tools, Collect Values). Then, you need to make this whole model iteration a "Sub-Model" inside your main model (you can drag and drop into your main model). The parameters will show up, and you can then add a "Merge" tool after the output paramater of this sub-model. This will merge ALL the outputs that the "collect values" tool collected back into one layer.
See the two attachments - The first one uses the iterator, which is then included as a sub-model in second graphic.