Redistricting opponents said they have 63,030 signatures, which have been turned in to the Maryland Secretary of State's Office, The Baltimore Sun reported.
That's 7,294 more signatures than the 55,736 required to put the map on the ballot for a referendum in November.
Republican critics have said the redistricting map approved by the Democrat-controlled General Assembly amounts to unfair, partisan gerrymandering to benefit Democrats.
Maryland Gov. Martin O'Malley, a Democrat, has received praise from the party nationally for creating a redistricting map that gives Democrats a good shot at adding a congressional seat.
About 9 percent of the signatures in a first batch last month were found to be invalid by the state Board of Elections. If that rate holds for the second round of signatures, those seeking the referendum still would have enough.
But the Sun said a higher percentage of signatures likely would be found invalid because of a last-minute push to get signatures.
If the state Board of Elections certifies the results, the Democratic party likely would challenge the board's ruling in court and get more signatures thrown out as invalid, the Sun said.