Why was there increasing congressional opposition to Roosevelt’s proposals during his second term?

There are two reasons that are generally given for this. 
First, there is the idea that the successes of FDR's first term had lessened the sense
of urgency felt by Congress.  Second, there was the court-packing plan that annoyed
Congress.

During FDR's first term, the Depression was at
its height and Congress was anxious to do anything FDR wanted to try to improve economic
conditions.  By his second term, things were better (though not by any means completely
good) and Congress did not feel the need to do whatever FDR
wanted.

Secondly, FDR had annoyed many in Congress with his
effort to "pack" the Supreme Court.  This made it seem as if FDR was trying to take more
power than was rightfully his.  This caused something of a backlash in
Congress.