Staff are still researching the cost of building the park, and they are expected to report their findings to the Chapel Hill Town Council on March 26.
Sonna Loewenthal, Chapel Hill assistant town manager, said Chapel Hill, like the rest of North Carolina, will be squeezed by the state's budget deficit, and no one is sure yet what this and next year's budget constraints will be.
The state is expected to keep some of the town's funds this year and might cut Chapel Hill's state revenue by as much as $700,000 for next year.
"We'll have trouble keeping some old programs running, and new programs will be under great scrutiny," Loewenthal said.
At the Town Council meeting Feb. 12, no one opposed building an area for leash-free dog exercise at one of five parks in Chapel Hill. Two residents, who took the floor at the meeting, spoke in support of the proposed park.
Even some residents who did not attend the meeting said they support the proposal.
"Everybody's got to have a place to walk their dogs," said Jayne Gregory, who lives on Kenmore Road near Cedar Falls Park. "It sounds like a good idea to me."
The possible locations for the dog park include three existing parks -- Homestead, Community Center and Cedar Falls. Two other parks that will be built later, Southern Community Park and Meadowmont Park, are other options for the Town Council.
Though no residents showed up at last week's Council meeting to voice opposition, council member Flicka Bateman said the Town Council received two e-mails criticizing the possible placement of the dog parks near residents' homes.