Daniel Cowart, 20, said his indictment should be dismissed.
A grand jury indicted Cowart and Paul Schlesselman, 18, on Nov. 5, charging them with plotting to kill Obama, possessing a sawed-off shotgun, carrying guns across state lines to commit crimes and planning to rob a licensed firearms dealer.
Cowart and Schlesselman are awaiting trial without bond at a northwest Tennessee jail, on lockdown in a two-man cell and separated from other inmates for their own safety.
In his petition, Cowart said the grand jury had two white members, while "21 were African-American or of another race or races." The jury, he said, could not "under the most modest constitutional scrutiny ... be considered fair, impartial and unprejudiced."
Prosecutors declined comment.
Authorities describe Cowart and Schlesselman as white supremacist skinheads and accuse them of plotting a robbery and killing spree in which 88 black victims were to be slain.
The spree was to culminate, authorities say, in an attack on Obama - with Cowart and Schlesselman decked out in white tuxedoes and firing guns from a speeding car.
No trial date has been set. Cowart and Schlesselman are expected to stand trial in the town of Jackson about 75 miles north of Memphis, because the crimes they are charged with allegedly occurred in that area.
"There had to be either a systematic exclusion of white people from that (grand jury) pool or there was some unexplained deviation in the composition of that pool by which you get two white people out of 23," said Joe Byrd, Cowart's attorney.
Byrd did not say how he knew the racial makeup of the grand jury. "That's the information I have," he said. "I'm not stereotyping anybody. What I'm saying is the law requires a fair cross section of the community and that didn't happen."
Byrd refused to discuss the charges against his client or his alleged affiliation with white supremacist groups.