Auditor General Caroline Gardner, who is responsible for ensuring public money is spent properly, made the claim one week after a report revealed a three-fold increase in the number of people delayed for more than four hours in A&Es.
The health service has rarely achieved the Scottish Government's standard to deal with 98% of A&E casualties in four hours.
A lower interim target of 95% was set in April last year in an attempt to boost performance by September this year.
Questioned by MSPs on Holyrood's Public Audit Committee quizzed on the issue yesterday, Ms Gardner said: "What we are seeing, and what we say in the report, is that there are indications of pressure in the system.
"We believe a number of boards will find it hard to meet the 95% target by September of this year."
Concern was raised at the meeting about a spike in activity across hospitals in the last 10 minutes before patients breach the target deadline.
More than 18% of admissions from A&E at the Royal Infirmary of Edinburgh were recorded just before the time limit passed.
Ms Gardner said extra work will be carried out to explore what is happening to patients during the course of their wait.
"We are planning some work," she said "As part of that we will want to talk to some patients again."
Scotland has 31 A&E departments which saw approximately 1.35 million patients in 2012-13 at a cost of about £163 million, Audit Scotland said in its report on May 8.
About 104,000 people waited beyond the standard four-hour target in 2012-13, compared with about 36,000 in 2008-09.
The proportion of people being seen within the four-hour target fell from 97.2% at the end of 2009 to 93.5% by December last year.
The report shows variation in demand at A&E across the country.
Gilbert Bain Hospital in Lerwick, Shetland, and the Royal Aberdeen Children's Hospital were the only two to meet the 98% target in each month of the financial year 2012-13. Most other hospitals failed in every month.
The report noted action is being taken by the Scottish Government and that the situation has improved in recent months.
The Government announced a national plan in February last year to improve emergency care.
The NHS plans to invest about £50 million in unscheduled care between 2013-14 and 2015-16.
Health Secretary Alex Neil said that there has been an 87% reduction in patients waiting over 12 hours.