There's a caucus in Congress for everything -- even a Congressional Ethiopia Caucus. It's composed entirely of Democrats and led by Rep. Mike Honda (15-Calif.), who supported Cindy Sheehan's ramblings this summer.
The Caucus has issued a statement on the violence in Ethiopia. Though not listed on Honda's website, the Sudan Tribune has a copy. It's not substantially different from the State Department position, calling for dialogue, "an independent commission to investigate the violence," and government restraint. The Democrats' statement also seems to equate the moral positions of the protesters and the government: "The use of violence, or attempts to incite violence are strongly condemned..."