The Native Hawaiian Bill in the US Senate is likely to be put to a vote in two days.
The bill starts a process for organising a native Hawaiian government.
Hawaii Senator Dan Akaka has persuaded Republican Senate leaders to hold a vote to close debate on the bill.
The Honolulu Star says the reports Akaka Bill was blocked a month ago by a group of Republicans, who say the bill is to give legal rights to people based on their race.
But advocates for the bill argue that it is based on recognizing those who were the first members of the Kingdom of Hawaii, which was overthrown by the US in 1893.