Harper has repeatedly said he first learned of the cheque on May 15, the morning after initial news reports were published on the deal to repay Duffy's improper expenses.
The Nanos survey asked Canadians how satisfied they were with the prime minister's explanation of what he knew about the cheque and when. Seventy-two per cent said they were dissatisfied or somewhat dissatisfied. Only 27 per cent were satisfied or somewhat satisfied.
"It is fair to say the prime minister has taken a 'strike,' at least, on this particular issue," Nik Nanos told CBC News Network's Power & Politics host Evan Solomon.
The survey also found a high amount of awareness about the Duffy-Wright matter, with more than 95 per cent of respondents aware of the controversy.
When asked to assign blame over the controversy using a 100-point scale, respondents assigned 43 points to Duffy, 32 to Harper and 25 to Wright.
But Nanos said the negative results for Harper in the Senate case won't necessarily damage his performance in the next election, scheduled for late 2015.
When asked which factor would be most important in assessing the prime minister's performance, 45 per cent of respondents said they would consider his track record on the economy, compared to 39 per cent who said they would focus on his handling of the controversy.
"We should not confuse anger, the hit that the prime minister is taking, the frustration of the opposition parties with ... a potential ballot-box impact," Nanos said.
The random survey of 1,000 Canadians was conducted between between June 8 and 11, before the RCMP announced it was investigating the Duffy-Wright deal. It was also completed before last week's CBC News interview with Senator Pamela Wallin about her expenses and before Senator Mac Harb was advised to repay more than $231,000 in expenses or face a more extensive audit.
Participants in the survey were randomly recruited by telephone and administered a survey online. The margin of error for a random survey of 1,000 Canadians is plus or minus 3.1 per cent, 19 times out of 20.
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