Here's a nice illustration from the European Central Bank's Jacob Ejsing and Wolfgang Lemkeon of how markets interpreted government rescue packages for banks across Europe:
The chart shows how the premia on credit default swaps for governments (i.e., the cost of insurance on government debt) shot up while premia for banks dipped over a tumultuous week in October 2008 when a host of rescue measures were introduced.
After the crisis's peak, sovereign CDS were much more responsive than bank CDS to news about the health of financial markets. In other words, the markets -- like most pundits -- saw the bailouts as a "risk transfer" from the financial system to taxpayers.