Olson, who died last month of a stroke, was the last Democrat to hold countywide office. He won his last election in 2012 with 68 percent of the vote. But Party Chairman Lynn Lindeman said the Democratic Executive Committee wouldn't be nominating a successor.
"We have no say in the process whatsoever," Lindeman said.
Gov. Rick Scott will appoint a successor for Olson, but his spokesman says there is no timetable to make an appointment and no decision regarding the party of the appointee.
Lindeman said he assumed that Republican nominee Ed Blommel would be appointed despite winning just 32 percent of the vote. Blommel could not be reached for comment.
A spokesman for the governor's office said three candidates have applied for the vacancy: Eileen Ferdinand, who served as Olson's chief assistant for the last decade, Matthew Abbott and Blommel.
State Rep. Mike Fasano, R-New Port Richey, has emerged as a potential successor. The longtime legislator has already had conversations with Scott's chief of staff regarding the position.
Fasano said he had been eying the tax collector post and planned to run for it in 2016, when Olson retired. Fasano returned to the Florida House this year because term limits barred him from seeking another term in the state Senate.
"It's something I was looking at down the road. Unfortunately, the position came open earlier than any of us expected," he said. "I would like to continue to do the good work he started. You know, I thrive on providing the best constituent service and customer service possible."
Though she has applied for the position, Ferdinand said she has made a commitment to Scott to ensure a seamless transition if someone else is appointed.
Ferdinand has been running the office since Olson's stroke in late June.
"Mr. Olson had given me all the authority to take care of signing checks and running the office in his absence," she said. "I worked closely with him for almost 11 years, and I know all the duties of the office. We have a competent staff that is customer service-focused."
Ferdinand said Olson's plan to open two new tax collector offices in Land O' Lakes and Zephyrhills are currently on hold. Olson had been looking for property in southeast and central Pasco to build new offices.
Olson closed the Zephyrhills office in 2011 when high winds ripped open the roof, resulting in severe water damage and mold growth.
"The issue with the Land O' Lakes office is that the volume of customers and number of driver's license applicants has increased," Ferdinand said. "We've also had a number of fender-benders in the parking lot. Mr. Olson wanted both offices to have driving courses on site."
The plan was controversial because Olson had planned to finance the new offices with the millions of dollars in excess fees his office collects each year - money that typically was turned over to the Board of County Commissioners.
"That's on hold now," Ferdinand said. "Obviously, it will be a decision made by whoever is the next tax collector."