On paper, no. We're all insured by the FDIC/NCUA up to $250k per institution (or account? I forget). In reality, I think the systemic risk means everyone has deposits on the line as the FDIC can't cover multiple bank failures.
in 2008-2010 the FDIC got on the phone and brokered sales of smaller banks to large banks, specifically because they needed to do their part to stave off disaster with their thin credit line. Congress didn't ask them to do this, they just got on the phone because they had live capitalization ratio data.