Teachers say the highest achievers are benefiting most from the programme, according to an Edinburgh University team who analysed responses from staff at 80 representative schools.
The research study says that the fresh focus on literacy and numeracy, backed by additional staff, in-service training and smaller classes, may not automatically narrow the gap between the most disadvantaged pupils and their peers. Teachers are more cautious than others about progress.
Dr Anne Pirrie, one of the lead researchers, warned a national conference in the capital last week that key expectations could be thwarted by classroom reality.
"If part of this is about fostering social inclusion, this could have a negative effect," she said. It was unclear whether the programme was about social inclusion or raising attainment for all.
Dr Pirrie said the high profile of early intervention meant that many schools were now making advances in the early stages of primary and improving attainment. But gaps could therefore widen.
Hard evidence on attainment will be available next year, once a second round of standardised testing is carried out on 2,000 P3 pupils in 64 Scottish primaries.
But Helen Fraser, senior lecturer at Edinburgh University, said teachers' comments should be listened to: "School staff say it's the highest achievers for whom the programme is having the greatest effect. Then it's the middle achievers, the most disadvantaged and the slowest achievers.
It's the same in numeracy."
"I think we must be slightly cautious that there's a bit of confusion what this programme is about," she added. Only 20 per cent of headteachers said the programme was actually about tackling poverty and the complex difficulties poor pupils face.
Encouragingly, 75 per cent of people interviewed - teachers, heads, learning support, nursery nurses and classroom assistants, psychologists and local authority staff - say that some or most P1 and P2 children are reading better than children in previous years.
All parties agree that early intervention is associated with net gains in attainment. Eighty per cent of council staff say it has been very or extremely effective for disadvantaged pupils. But only 40 per cent of P1 and P2 teachers agree with them. There is no difference between teachers on the effectiveness for boys and girls.
The programme is having considerable benefits for teaching, the researchers confirm. Over six out of ten P1 and P2 teachers say they are more confident in their professional practice. The vast majority of all groups believe there is more time on direct teaching of literacy. And a significant majority think more is expected of pupils.
Nearly half the teachers (46 per cent) say their workload has increased, but 58 per cent report increased enthusiasm for teaching. Almost seven out of ten teachers are more aware of research on literacy.
Dr Pirrie said teachers did not believe pupils were under more pressure.
There was a buzz about classrooms and "a much more holistic sense of enjoyment".