Local governments worried about the extra costs associated with changes the General Assembly made to the Virginia Retirement System last week may get a bit of a reprieve.

Lawmakers passed a bill requiring local governments to give their employees a 5 percent raise to offset their workers having to pay a 5 percent contribution into the retirement system. (Currently, governments pick up the whole tab).

State officials say all that should equal out in the end. Not so fast, local government say.

Localities complain that they actually will have to pay thousands, and in some cases, millions of dollars to pick up the costs associated with their employees earning more (payroll taxes and higher VRS contributions).

For example, Prince William County, the second largest county in Virginia, estimates the change will cost it $5 million, Board chairman Corey Stewart said.

But several local government learned Wednesday that Gov. Bob McDonnell (R), who has made pension reform one of his top priorities, will amend the bill so localities can incur those costs over five years.

Legislators will consider McDonnell’s amendments to bills on April 18. “We are open to amendments to that effect and will be discussing the matter further in the weeks ahead,’’ McDonnell spokesman Tucker Martin said.

The General Assembly also passed another pension change that would usher in a hybrid retirement plan for new state employees, local employees and teachers.