Some 65 percent of the general public, including 52 percent of Labour supporters, think he should leave by early next year.
Almost half of Labour voters surveyed in February said he should stay on until 2008 or later, while just 21 percent think so now.
The proportion of Labour supporters who thought "the wheels are falling off the coach" has jumped from 10 percent in February to 35 percent in the latest survey.
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