LYNN, Mass. (AP) – Kerry Healey warned the election of Democrat Deval Patrick would usher in an era of one-party rule on Beacon Hill, while Patrick said Healey sounded increasingly “desperate” as the candidates for governor entered the last full week of campaigning.

Healey, stumping for votes Sunday at a Halloween costume parade at Boston’s Castle Island, said only she, as a Republican, could hold back the Democratic appetite for higher taxes, lax crime laws and a poor business environment.

It’s a theme Healey hopes will help her close a more than 20-point gap with Patrick in the final week of the campaign.

“People have perhaps gotten to the point where they take balance on Beacon Hill for granted. They just assume that there’s going to be somebody on Beacon Hill who’s going to speak out in favor of the taxpayer,” Healey said.

Republicans have held the governor’s office for the past 16 years, while Democrats have ruled the Massachusetts House and Senate.

“We’re going to lose that if Deval Patrick is elected,” she said. “There’s a lot of danger to one-party government.”

Patrick, speaking to about 500 supporters at North Shore Community College in Lynn, said Healey’s argument is a red herring designed to distract voters.

Patrick said Massachusetts has little to show after four years of “balanced government” under the administration of Gov. Mitt Romney and Healey, his lieutenant governor. The state has lost population, fallen to 42nd in the country in job growth and “radically defunded” support for public colleges and universities, he said.

“That all came and is coming during this so-called balanced government,” Patrick said. “Forget about party. That’s the point. I’m not just running to be governor of Democrats. I’m running to be governor of the whole commonwealth.”

He added, “there’s a lot that seems desperate about her campaign and seems about changing the subject.”

Independent Christy Mihos and Grace Ross of the Green-Rainbow Party are also running for governor, but polls have shown both stuck in the single digits in terms of voter support.

As they gear up for the final push, both major party candidates had clear tasks ahead. Healey is faced with overcoming Patrick’s hefty lead in the polls while Patrick has to guard against his backers being overconfident and taking the election for granted.

That momentum grew Sunday as Patrick won the endorsements of three newspapers: The Boston Globe, the Telegram & Gazette of Worcester and the MetroWest Daily News of Framingham. Healey called the endorsements “not surprising.”

Confidence mixed with caution was a message Patrick emphasized during his 20-minute speech, as he joked about the early days of his long-shot campaign, and urged supporters to “go get ’em.”

After the Lynn rally, Patrick headed to another rally in Healey’s hometown of Beverly and then onto Methuen.

Healey and Patrick also used the day to take shots at each other.

Healey again tried to push Patrick into a one-on-one debate, saying “he wants to simply get into office without telling anybody what it is, in fact, that he intends to do.” Patrick said Healey “has a million excuses for why the campaign she’s running is not her responsibility.”

Patrick also said he hopes voters “fire” him and running mate Tim Murray in four years if they don’t deliver on their promises.

One of those who turned out to hear Patrick was Esther Vargas, 29, an office manager at a charter school, who was urged to come to the rally by her 9-year-old daughter, Raeshean.

Vargas was impressed.

“I think he’s great. If he hadn’t convinced me yet, he’s convinced me now,” the Lynn woman said after the rally. “He’s seems to be very down to earth, in it for the little people. He seems to understand that we might not have it all, but he’s going to help us out.”

Her daughter, Raeshean, said she became interested in Patrick after watching political advertisements and listening to his ideas.

“I think he knows what he’s saying and that he knows what he wants to do and he wants to help everybody and he’s in it for a good cause,” she said.

Healey also picked up support on Sunday, winning the backing of a Democratic lawmaker, Rep. Brian Wallace, who represents the South Boston neighborhood.

Wallace said he’s never spoken to Patrick, but when he needed help saving a drug treatment center or opening a high school for young people trying to stay off drugs, Healey was there.

“As far as I’m concerned her word is good. I think she’s honest … and I also like (Healey running mate) Reed Hillman. I served with him in the Legislature and he’s a standup guy. That’s why I’m standing up.” Wallace said. “With me it’s all about loyalty. She’s been good to me and she’s been good to my community … when we needed her, she was there.”

Healey has her work cut out for her. Polls released this past week by WHDH-TV and Suffolk University, as well as WBZ-TV and The Boston Globe, showed Patrick leading Healey by 25 points and 24 points, respectively.

The lieutenant governor’s unfavorability rating has also spiked, with poll respondents citing her use of negative advertising.