Should the United States take a more active role in support of universal human rights?

This depends on what sort of a more active role is
envisioned.  If we are envisioning a United States that uses military force or economic
sanctions to try to cure all of the human rights problems in the world, then the answer
is no.  If we are talking about putting more diplomatic efforts into supporting human
rights, then the answer may well be yes.

The US cannot
afford to be too aggressive in support of human rights.  For example, the US is in no
position to punish China either militarily or economically for China's lack of concern
for the human rights of Tibetans or of the Falun Gong, or of any political dissidents. 
It may be a good idea for the US to put more effort into persuading countries like China
to show more respect for human rights, but anything more than that is simply
impractical.