Those who believed Mr Key was performing poorly went up by more than 6 points in the Reid Research poll to 32 per cent.
Although Labour slipped as well in the Reid Research poll and leader David Shearer had low support in in both polls, Labour and the Greens would have been able to govern based on the One News results.
The effect of the joint release by the Greens and Labour of the NZ Power energy policy last week was not measured as the polls had closed.
Issues over the GCSB dominated before the poll after Mr Key confirmed he had directly contacted a school acquaintance, Ian Fletcher, to apply for the job, and was then blindsided by the leak of a report into the GCSB which showed the agency had possibly illegally spied on about 85 New Zealanders on behalf of other agencies.
Last week, Mr Key released plans to change the law to allow that type of espionage. The same-sex marriage bill was also a major feature over the polling period and the Conservative Party, which opposed that bill, gained a small lift in support.
Mr Key said yesterday he was taking the polls with "a grain of salt", and the 3 News poll showed New Zealanders had seen through Labour's attempts to dent his credibility over the GCSB saga.
But the One News poll reflects a similar trend in the Roy Morgan poll released last week and will be a concern to National.
National will also increase its efforts to sow doubt about the economic management of Labour and the Green Party. It has described the proposal to set up a single Crown-owned agency to buy power from generators to sell to retail companies - a policy estimated to save households about $300 a year - as similar to North Korea.
That announcement could also hit the expected share price for Mighty River Power and has forced the state-owned company to assess whether it needs to change the investment prospectus to mention the policy.
Mr Key said yesterday that Mighty River Power had been looking at that over the weekend, but was yet to reach a conclusion.
NZ First did not make it over the 5 per cent threshold on either poll but was still within reach and could be needed by National in 2014.
Although it has said it will support new GCSB legislation, leader Winston Peters has also said he wants to renationalise Mighty River Power using KiwiSaver funds and the Super Fund.
Mr Key said yesterday he would give an indication of which parties he could work with closer to the election next year.
Latest polls
One News
* National 43 per cent
* Labour 36 per cent
* Preferred PM: Key 39 per cent (down 5 per cent),
* Shearer 15 per cent (no change)
3 News
* National 49 per cent, Labour 30 per cent
* Preferred PM: Key 38 per cent (down 3 per cent),
* Shearer 10 per cent (no change).
