Sir Lynton Crosby has cautioned Remain supporters against "complacency" ahead of the EU referendum.
The election strategist made his warning after an ORB poll, out this morning, showed a slight increase in support for a so-called Brexit during President Barack Obama's visit.
But while 51 per cent of those polled said they supported remaining in the EU, a greater proportion - 57 per cent - said they expect Remain to win the vote in June.
Meanwhile, 46 per cent supported a Brexit, compared with 21 per cent who expect it.
Crosby said: “This vast gap in expectation means that the Remain campaign is still largely at risk of voter complacency. Many of their supporters will expect to win the referendum and thus fail to recognise the significance of their own vote.”
The ORB results, commissioned by the Telegraph, reported a slight increase in support for a Brexit - from 43 per cent in results released last week to 46 per cent - during Obama's visit, despite the US president speaking out in favour of Remain.
Crosby said this could be because some “people may not take much notice of what an outsider has to say”. He also suggested it may take a while for Obama's warnings to “wash through”.
Writing in the Telegraph, Crosby said the referendum “marathon has barely begun”.
He added: “While this ORB poll was conducted over the course of [Obama's] visit, it suggests the president's view has not (and indeed may not) directly influenced voters, but may well be contributing to the overall tone of the campaign and voter's views that they have heard more from Remain.
“For now, both camps must continue to stay the course with respect to their messaging and focus on consolidating their base support for the referendum.”