The poll was conducted by ABAC Social Innovation in Management and Business Analysis Centre.
Its respondents comprised 1,459 residents of Bangkok and its suburbs.
The survey was conducted between last Thursday and Saturday.
Dr Noppadol Kannikar, director of the centre, said it found 45.4 per cent of the respondents supporting the government of Prime Minister Samak Sundaravej while 36.8 per cent did not support it. The remaining 17.8 per cent gave no comment.
He said 77.8 per cent of respondents said the government should rush to tackle the hardship of the public before helping Thaksin.
Only 4.6 per cent said the government should give priority to assist Thaksin.
The rest of the respondents said the government should try to solve the problems of the people and Thaksin at the same time.
The survey also found 53.6 per cent of respondents supported a proposal to have former Thai Rak Thai executives appointed as board directors at state firms.
Some 45.6 per cent disagreed while 0.8 per cent made no comment.
Noppadol noted the government should not appoint former Thai Rak Thai executives to sit on the board of state firms because a high percentage of their opponents could cause trouble.
On a scale of 10, the survey found the confidence level among people polled on the government's ability to solve the economic problems stood at 4.31.
Their confidence level about the government's ability to curb drug trafficking stood at 4.26.
Respondents gave scores of 3.76 and 3.62 on the government's ability to prevent rifts among coalition partners and on stopping graft respectively.