The BLM's website geocommunicator.gov is down and I'm wondering if anyone knows of a second source for PLSS shapefiles.
The state BLM office pages often have a version of the data. Colorado for example. However I've found that version may or may not match the one on Geocommunicator - as the data stewards the state version may be more up to date / recently revised (and I've seen the reverse too, where the communicator version was more recent than the state's). This page lists some of the offices, but note the links aren't all current/working (the Colorado one went to a broken GCDB page). It might be faster to just Google "[your state] blm gis data".
This assumes you specifically want the CadNSDI shapefiles, and all the details and attributes that go with them. If you just want a township/section grid, http://datagateway.nrcs.usda.gov/ has that data at the county level (as in, even if you get it by state, you'll still get one file for each county). If you're only looking for one county, county websites/GIS department downloads sometimes provide township and or section level data. I can't recall seeing any source other than CadNSDI that had sub-section level data though.
Like Chris W mentioned, http://datagateway.nrcs.usda.gov/, is another resource option for PLSS data. IIRR NRCS pulls a copy from Geocommunicator/BLM, stores and distributes it through the datagateway.
Couple things to note, on the datagateway main page, don't use the PLSS download link to the left under browse by subject. It's take you to the geocommunicator page.
Rather, click on the green order button. Go through the various menus to order the data.
The public doesn't need a log in for some of the data housed there. PLSS being one of them.