Even with no pay raise for city employees, Lawrence City Hall is facing a $1.6 million budget deficit in 2011.

Such a hole may cause city commissioners to do something they’ve been loath to do thus far in this recession: Dip into their savings account.

At a Monday afternoon study session, commissioners contemplated passing an unbalanced budget for 2011 in order to avoid either a property tax rate increase or significant cuts to city services.

“This could be the year that we have service cuts the public really notices,” said Mayor Mike Amyx. “I don’t want to say that for sure yet, but it could happen.”

Amyx told commissioners on Monday he likely would be willing to take about $825,000 out of the city’s fund balances — the equivalent of a savings account — to make some service cuts less likely.

Other commissioners, though, said that idea concerned them.

“I’m uncomfortable going forward without a balanced budget until I see something that says we’re in a different trend,” Commissioner Lance Johnson said. “I haven’t seen any signs that says this economy is going to get any better. The really rainy day could be another year or two years from now.”

That left commissioners contemplating possible areas to cut. No decisions were made, but discussion did turn to whether commissioners could afford to fund outside agencies — like service agencies ranging from Health Care Access to The Boys & Girls Club — at historic levels. City Manager David Corliss’ early numbers call for funding outside agencies at their 2010 levels. But some commissioners said they may need to consider reducing the funding.

“I’m just disagreeing that we take outside agency funding completely off the table,” Commissioner Rob Chestnut said. “I don’t think we can take anything off the table yet.”

Commissioner Aron Cromwell said cuts to many nonprofits during a time when the economy is sputtering concerned him.

“I would fight hard against that,” Cromwell said of social service cuts.

In other budget news:

• Prospects of a pay increase for city employees did not appear bright. Corliss built his early budget on the assumption that there would be no pay raise for 2011. This year, city pay raises averaged 1.25 percent for most non-union employees, while members of police and fire unions were eligible for a 5 percent increase.

• Staff members presented a plan that would raise water rates by 6 percent in 2011 and sewer rates by 2 percent. Commissioners were shown a plan where rates could be held steady for 2011, but it would require several major repair projects to be postponed for at least a year.

• Corliss’ early budget numbers assume some bounce back in the economy. Corliss is projecting that sales tax collections will increase by 2 percent over 2010 numbers. Commissioners weren’t entirely convinced that would happen, but agreed to take up the subject in early June when more data are available.

Commissioners must approve a 2011 budget by late August.