The poll, released on Wednesday night, showed a 22-percent turnaround since the question was last taken after the 2012 presidential election. At that time, 63 percent of GOP voters said he had a strong future in their party.
The New Jersey governor, seen as a possible presidential contender in 2016, apologized and has sought to move on.
A battery of polling in the last week has shown Christie's approval ratings dropped after the bridge scandal.
Both the state legislature and the U.S. attorney in the state are looking into the matter.
Christie has denied he knew about the closure plan and fired his deputy chief of staff, who was linked to the incident in emails.
Overall, 44 percent of voters think he does not have a strong future in the Republican Party — an 18-point drop since the last time the question was tested.
Another 38 percent think he does, while 18 percent do not know.
Sixty percent of voters said they have been following the scandal closely, while 38 have not.
The poll surveyed 1,010 registered voters and has a 3-percent margin of error.