Members of the BBC's Question Time audience told Tony Blair that they found it difficult to make an appointment to see their GP more than two days in advance, and blamed "targets" which were set by the government. Mr Blair expressed surprise and promised to investigate.
There is a fierce debate about target-setting in the NHS.
The Conservatives and Liberal Democrats argue that the use of targets reduces clinical freedom, while Labour says that targets are necessary to achieve improvements.
Conservative health spokesman Andrew Lansley said: "Mr Blair is out of touch with what is going on in the NHS. It is his government that set the targets which distort the way GPs want to run their practices."
And Liberal Democrat health spokesman Paul Burstow said: "The political targets are fatally flawed - they miss the point and let patients down."
The NHS Plan in 2000 pledged that by 2004 all patients should be able to see a GP within 48 hours. According to government figures, the target is being met in 99.9% of cases by the end of last year, compared with 50% in 1997.
GP numbers are up 6% since 2001, and the government says it has invested £900m in building or refurbishing GP premises, and recently announced plans to make it easier for GPs to expand the services they offer.
But the British Medical Association, which represents doctors, says the government should "eschew politically attractive, but superficial and potentially flawed policies such as 48 hour access".
Dr Hamish Meldrum of the BMA said that if more appointments have to be kept clear for those patients who want an appointment within 48 hours, there will be necessarily fewer appointments available for those who want to book in advance.
And Patient Concern, which lobbies on behalf of NHS patients, says it has had complaints from all over the country from patients who can longer book appointments to fit in with work or family schedules or book to see their own GP.
It says it has been campaigning on this issue for a year, and that the Department of Health has tried but failed to stop primary care trusts from implementing such policies.
The government claims that the number of GP surgeries which do not allow any advance booking fell from 7.7% last December to 3.6% in March. The provisional figure for April is 2%.
And the NHS chief executive wrote to NHS primary care trusts at the end of last year telling family doctors it was unacceptable to stop forward appointments in order to leave time free for patients who needed to see them urgently.
The problem that the Question Time audience complained of definitely exists, although it is difficult to measure to the scale of the problem.
However, the government accepts that in some areas one underlying cause of the problem is a continuing shortage of GPs.
One possible change the government might make is a modification to its 48-hour target, with perhaps only 80% of patients, rather than 100%, having to been seen within two days.
Health Secretary John Reid appears to be moving away from target-setting in some areas, although he introduced new targets for breast cancer screening during the election campaign.