Labor looks unlikely to get the 39 Senate seats it need to introduce its tax reform agenda, according to Australia Institute polling that also shows Clive Palmer could end up with no seat at all after spending $60 million on advertising.

The polling shows that Labor would win at most 28 Senate seats and the Greens, which largely support Labor's agenda, are likely to win seven to nine seats, bringing the total to 37, just short of what is needed to control the senate.