The state Court of Appeals may invalidate changes to the state constitution voters approved last year.
The changes set up a requirement for Voter IDs and made limits on income tax rates virtually permanent.
The NAACP is asking the court to void those measures, saying the state's political boundaries were so racially gerrymandered that the Republican-controlled legislature that put them on the ballot lacked validity.
Attorneys for legislative leaders say if the lawsuit succeeds any law passed by the General Assembly for years could be challenged.
A lawyer for the NAACP argues that the GOP lawmakers knew their legislative districts cheated black voters and would be overturned.