A televised debate Tuesday night marked the latest — and perhaps the last — major attempt by New Haven mayor and Democratic gubernatorial candidate John DeStefano Jr. to paint his Republican rival, Gov. M. Jodi Rell, as ineffective and insincere.

Recent polls indicate that Rell is still enjoying a double-digit lead over her opponents with less than three weeks left before Election Day. The hour-long debate exposed occasional personal animosity between the candidates but at other times failed to show major policy differences between them, especially on national issues such as high gasoline prices and education funding.

Rell began her opening statement by pointing out that she could have chosen not to run in the gubernatorial race. She said a reporter recently asked why she did not retire now, at the height of her popularity, in order to spend more time with her grandson.

“You know, that all sounds very good, but I have to tell you we have accomplished an awful lot in the last two years by returning ethics and honesty to state government,” she said. “But there is much more work to be done, and I want to built on our successes.”

DeStefano disputed Rell’s record and principles. He chastised her for only suspending, rather than firing, her friend and chief of staff M. Lisa Moody, who gave tickets for a Rell fundraising event to officials at the Capitol building despite policies barring such campaign tactics. Rell responded that no law had been broken, as the rule Moody violated was Rell’s own and not imposed by the state.

Prior to the televised debate, Rell also ran her campaign commercial, which featured dozens of young children, including her grandson. Political commentators have said Rell’s campaign has effectively portrayed her as a steady and moderate grandmother, a move they said has increased her appeal among liberal and moderate voters.

During the debate, DeStefano questioned Rell’s track record on policies affecting Connecticut youth. He also said the governor has done little to make higher education affordable, offered her inaction as explanation for why university faculties support Destefano’s candidacy.

In response, Rell pointed to increased grant and scholarship accessibility, her proposal for a tuition freeze, and the fact that 68 percent of high-school graduates choose to attend an in-state college.

DeStefano also reiterated the theme of many of his recent campaign ads: Rell’s reluctance at their last debate to name the worst mistake she made while in office. This week, Rell recanted her original response to that question, jokingly calling it “probably the worst mistake” she’s made so far. She went on to say that her handling of her proposed cut in automobile taxes was actually her greatest misstep.

There was one unexpected guest at the debate. At the stroke of seven, as the program was about to begin, a political advertisement for one of the gubernatorial candidates came on screen — and it wasn’t for DeStefano or Rell. It was Green Party candidate Cliff Thornton, who nearly emptied his war chest on the last-ditch publicity effort. Surrounded by demonstrators chanting, “This is not democracy,” Thornton protested the television station’s decision to exclude him from the debate.

“We want to talk about issues, but these candidates are not going to talk about them,” he said.

According to the latest Quinnipiac poll, released in late September, Rell is leading DeStefano 63 percent to 30 percent. 42 percent of Democrats and 67 percent of independents said they were planning to vote for the Republican incumbent.