THE Gillard government will enter the Christmas break haemorrhaging votes to the Greens, according to a poll which also shows most of the population supports gay marriage.

The latest Herald/Nielsen poll finds Labor's position is slightly worse now than at the election on August 21 and if a poll were held now it would most likely lose.

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It finds no change from the last poll a month ago, with the Coalition leading the government on a two-party-preferred basis by 51 per cent to 49 per cent.

Labor's primary vote is relatively unchanged from a month ago at 35 per cent, compared with 43 per cent for the Coalition and a still healthy 13 per cent for the Greens.