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.