The great crested newts were found in the site of the Earl Shilton bypass.
The £15m project, due to finish this year will not now be ready until next February, costing an extra £1.2m.
Another £500,000 needs to be spent on steps to stop the rare amphibians returning and on traps to catch them when hibernation ends this spring.
"If we are talking about a small number of newts costing £1.7m that is unacceptable"
Leicestershire County Council has a legal obligation to ensure the newts and their habitat are protected.
A spokesman said: "Low numbers of newts were found - between one and 10 in the three ponds where evidence of their presence was found."
He added that the £1.7m cost was "only approximate" and would depend on how long the contractor was delayed.
Council leader Councillor David Parsons said: "I think the public will take it enormously badly and I think we have got to have a change in the law.
"If we are talking about a small number of newts costing £1.7m that is unacceptable."
The route is about three miles (5km) long and follows the corridor that links the A47 perimeter road from a new roundabout at Carrs Hill to the A47 Leicester Road.
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