Barack Obama is taking on health care, financial regulation, torture and environmental policy. He’s also revamping the White House art collection.

The Obamas are sending ripples through the art world as they put the call out to museums, galleries and private collectors that they’d like to borrow modern art by African-American, Asian, Hispanic and female artists for the White House. In a sharp departure from the 19th-century still lifes, pastorals and portraits that dominate the White House’s public rooms,...