Zimmerman was acquitted July 13 on second-degree murder charges in the February 2012 shooting death of Martin, an unarmed black teen, in Sanford, Fla.
The boycott, threatened by the Rev. Jesse Jackson, is seen as a means of overturning the state's stand-your-ground law, The Hill reported Saturday. Rep. Lacy Clay, D-Mo., said he supports the boycott as part of a "multi-pronged strategy" that includes legislation and getting laws overturned by the courts.
A drop-off in revenues "will get the attention of the powerful," he said.
Rep. Barbara Lee, D-Calif., said she would support "whatever it takes to get these stand-your-ground laws off the books."
Jackson said Thursday if the U.S. Department of Justice does not file federal civil rights violation charges against Zimmerman, he would consider launching a boycott "to isolate Florida as a kind of apartheid state."
Thousands of people across the United States were expected to gather in front of federal buildings Saturday for "Justice for Trayvon" vigils, The Miami Herald reported.
The events, scheduled in at least 101 cities, are intended to pressure the Obama administration to file federal civil rights charges against Zimmerman.
The National Action Network, founded by the Rev. Al Sharpton, one of the organizers of the vigils, will broadcast videos of the vigils on its website.
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