The race could be crucial for state Democrats, who are eager to wrangle control of the Senate from Republicans but have a limited number of winnable seats statewide, political experts say.
So far, Cickay, 59, has shown little desire to leave the race, saying he's gotten a positive response while campaigning.
"I start something, I finish it," he said in an interview. "I feel an obligation to these people that voted for me. . . . I feel I owe it to them to finish."
Rendell said he called Cickay about 10 days ago, telling him that "people were impressed with Shaughnessy" after her race, and that he believed a female candidate had a better shot at winning that district. When Cickay indicated he wanted to remain in the race, Rendell said he respected the decision and wished Cickay luck.
Hughes declined to say whether he asked Cickay to step aside, but added that "we want to field the best candidates in the best seats."
John Cordisco, chairman of the Bucks County Democratic Committee, said simply, "As far as I'm concerned, at the moment, Steve Cickay is the candidate."
Naughton, through her previous campaign manager, declined to comment.
Cickay, a retired information-technology employee with the Army, Navy, and Labor and Treasury Departments, ran unopposed for the Democratic nomination in Pennsylvania's 10th Senate District.
Cickay said he was asked to run this winter by local Democratic leaders, including Cordisco.
Passionate about many topics, including raising the minimum wage, expanding Medicaid availability, and increasing investment in education, Cickay said he figured he could advocate for those issues in Harrisburg and decided to join the race.
"I was the only guy, and I stepped forward," he said. "I was proud that [Cordisco] supported me, and I've worked hard."
Unseating McIlhinney in November will be a challenge.
McIlhinney has deep political roots in the area, having served as a Doylestown Borough councilman and state representative before becoming a state senator in 2007.
One Democratic poll from March, obtained by The Inquirer, showed McIlhinney leading Cickay by 16 percentage points.
And Cickay had only $1,717 in cash on hand as of June 9, according to campaign records, compared with more than $150,000 for McIlhinney. Cickay acknowledged that raising money has been difficult.
All those reasons would motivate Democrats to try "to maneuver in a way to make that race as competitive as possible," said Chris Borick, a professor of political science at Muhlenberg College.
Borick said he was unaware of any attempt to remove Cickay from the race, but added that McIlhinney's district is coveted by Democrats, since it's one of the few across the state they can realistically win.
With Gov. Corbett facing a difficult reelection campaign, Borick said, Democrats "probably would like to have [Naughton] in this election cycle, where there's at least an outside chance where they could take control of the state Senate."
Naughton lost May's Democratic primary for Bucks County's congressional seat by a few hundred votes to Kevin Strouse, a former Army Ranger and CIA employee.
Naughton performed well in central Bucks County, the territory McIlhinney represents.
And Naughton's congressional campaign had just under $158,000 in cash on hand April 30, federal records show. Whatever money remained after the May 20 primary could be transferred to an account supporting Naughton's state candidacy, according to Lawrence J. Tabas, a lawyer who specializes in election law.
Still, whatever lobbying is taking place on her behalf, Naughton can't run as a Democrat unless Cickay drops out.
Cickay said he's in the race until the end.
"You'll be hearing from me," he said. "Now and through Nov. 4."