By a majority of 46% to 35% they said the principle of the change - dubbed a "bedroom tax" by critics - was "only fair", the ComRes survey for the Sunday People showed.
But clear overall majorities said that its implementation should be delayed for a rethink on how to implement it (52%), that it should only apply if people refused smaller homes (60) and that it should not apply at all to Army families with children away on active service (77%).
Out of the 2,002 UK adults interviewed online by ComRes on 13 and 14 February 2013, 27 percent of pollers believed the Conservatives could be trusted to make correct economical decisions, compared to 20 percent of people who polled for Labour leader Ed Miliband and Shadow Chancellor Ed Balls.
Here is a breakdown of the figures:
I trust David Cameron and George Osborne to make the right decisions about the economy
Agree 27% (+2) Disagree 51% (-4) Net agree -24% (+6)
I trust Ed Miliband and Ed Balls to make the right decisions about the economy
Agree 20% (-1) Disagree 55% (+3) Net agree -35% (-4)