The Chronicle of Philanthropy
has a nice article explaining how the U.S. Federal Government shutdown could affect non-profit organizations, including those receiving federal grant funds.
The article points out that many staff salaries at non-profit organizations are dependent on money generated from federal grants. Those positions may be in for short or longer term elimination. Interestingly, these funds may end up being distributed at a later date.
Advice for non-profits included "keep a careful tally of how the shutdown adds to your costs and prepare to make a claim to recover those expenses post-shutdown".