Senators Elizabeth Dole and John Edwards both supported the bill.
The measure would correct legislation passed by Congress in 1956 that effectively denied benefits to the tribe.
With some 55,000 members, the tribe is one of the largest tribes in the nation that doesn't have federal recognition.
The tribe, native to Robeson County, has tried for a century or more to get federal recognition.
Dole said recognition for the Lumbee was a matter of fairness. Federal recognition could bring opportunities for economic development, housing, education and health care to the tribe.
Leaders of the tribe attended a committee hearing last month in Washington.
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