Are there are any good lower bounds for the number of spanning trees for a *connected* graph $G$ in terms of (for example) number of edges $E$ or number of vertices $V$ ? 

Are improved bounds available if one knows the number of *bridges* of the graph? (A bridge, aka a cut-edge, is an edge whose removal disconnects the graph)

EDIT:

Here is a simpler statement of the question. What is the minimum number of spanning trees possible for a graph with $m$ edges and $n$ vertices which is (1) 1-edge-connected or (2) 2-edge-connected?