As Wright made his way out of a hearing Tuesday in Raleigh, he was asked if he was going to resign. He said he had no intention, but others say he should.
Wright is accused of spending about $250,000 of campaign money on personal items, as well as hiding contributions from executives connected with the Hugo Neu landfill.
Wright ultimately could be charged with one or more felonies.
The "Wilmington Star News," on its editorial page, is calling for the Democrat to step down from his post representing portions of New Hanover and Pender counties. State Senator Julia Boseman, also a Democrat, says she agrees.
WECT spoke with Democratic Party Chairman Jim Morgan. He says the party isn't ready to take a position.
"Our response depends on what happens in the next few weeks and how Representative Wright responds to the allegations."
As of now, it's up to the Wake County District Attorney as to whether the case is taken to court. It's unclear when that decision will come.
Reported by Sarah Warlick