The additional money would be used to pay for increased construction costs, Bruchey wrote.
The $300,000 Bruchey requested for the coming fiscal year would go toward demolition of The Video Store, widening of the alley behind The Alexander House and creating an open plaza, Bruchey said.
The alley off East Washington Street will serve as the main entrance to the parking deck.
Bruchey wrote that the improvements will allow for two-way traffic to and from the deck.
"It will also open the area off the alley to more visibility and openness and will remove a blighted building in the downtown," he wrote.
Bruchey said the cost of the parking deck increased because of unexpected problems during construction.
"We found that there was no rock where we needed it and rock where we did not want it," Bruchey wrote.
To fix the problem, a "mini-piling" system was constructed to provide an adequate foundation for the deck, which increased costs, he wrote.
The deck's total cost is $3.55 million, according to Bruchey's letter.
The deck was proposed to cost $2.4 million when the commissioners voted 3-2 in February 2004 to give the city $600,000. Commissioners Vice President William J. Wivell and Commissioner John C. Munson opposed the contribution.
Snook said Tuesday that the commissioners would have to set up a time to discuss the request.
City Finance Director Al Martin, who attended the commissioners meeting, said additional help from the county would help prevent significant parking rate increases.
The monthly rate will be $52.50, he said.
Commissioner John C. Munson said the county recently voted to raise water and sewer rates and landfill fees to pay for those services and questioned why the city wouldn't do the same with parking rates.
Martin said that if the city raised parking rates too much, it might cause "consumer resistance" to parking downtown.
The deck, in the Arts & Entertainment District, is set to open in July or August, Martin said.