Updated

The fight over the Fighting Sioux is headed for the ballot box in North Dakota.

Supporters of the nickname for University of North Dakota sports teams, which critics say is offensive to Native Americans, appear to have more than enough signatures to put the question to voters. Lee Ann Oliver, an election specialist for North Dakota Secretary of State Al Jaeger, told FoxNews.com that the supporters had 1,449 more signatures than necessary to ensure a June 12 vote on the issue. At least 13,452 signatures are required.

"It's a done deal unless arguments on Thursday tell us something else," Oliver said.

The North Dakota Supreme Court is scheduled to hear arguments on the case Thursday. The state's Board of Higher Education has said the law -- which mandates the university to use the Fighting Sioux nickname and American Indian head logo -- is unconstitutional. The board is suing Jaeger in an attempt to block the vote in June.

In February, the university's president announced the school would resume using the nickname and logo to respect the state's referendum process, which required that the pro-nickname law be in effect while the state reviewed more than 17,000 signatures submitted to Jaeger's office.

"I want to reaffirm our respect for the laws of the state and the processes guaranteed under the North Dakota Constitution," Robert Kelley's statement read.

NCAA officials have said the nickname and logo are demeaning to American Indians. In 2006, the NCAA called on 19 schools with American Indian nicknames, logos and mascots to change their "hostile and abusive" nicknames or obtain permission from local tribes to keep using them. Most changed their names, although the Florida State Seminoles and the Central Michigan Chippewas were among the schools that got tribal permission to keep their nicknames.

The Associated Press contributed to this report.