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“I wouldn’t dismiss the numbers out of hand, but we’ve seen governors across the country whose numbers are not in good shape. But we’re still talking about Massachusetts. It’s going to have to be a set of extraordinary circumstances for Republicans to win,” said elections analyst Nathan Gonzales, who closely tracks governorship races for the Rothenberg Political Report.

“If we get to next year and Patrick’s numbers are low, he may have a primary challenger. He’s more vulnerable in a primary than in a general election,” he said.

In fact, Democratic state Treasurer Timothy Cahill has been talking openly about challenging the governor in the primary. Harvard Pilgrim Health Care executive Charles D. Baker, a Republican, is considering the race, but no major Republican figure has come forward as a likely opponent thus far.

Still, Republican campaign officials note that Republicans had a 16-year run of governorships in the state before Mr. Patrick won. “Massachusetts voters are beginning to recognize that Deval Patrick is not getting the job done. The state’s political history shows they are more than willing to go for a Republican governor,” Mr. Schrimpf said.

Former Democratic National Committee Chairman Steve Grossman, a Boston businessman who is close to Mr. Patrick and met with him Friday, said, “He is far less concerned about momentary blips in the polling numbers and more concerned about people’s lives. I predict he will be re-elected.”

Still, Mr. Grossman acknowledged, “There is a general level of unhappiness in the land and about people’s view of government. Even the president’s numbers have shown significant slippage,” he said.

A Survey USA poll of 600 adults for WBZ-TV earlier this month showed his disapproval rating ballooning to 69 percent, with only 28 percent approving of his job performance.

“His numbers are atrocious. He has the Democratic state Treasurer who is thinking of running against him. He’s in a lot of trouble when he’s not getting respect from his own party,” said state Republican Chairwoman Jennifer Massour.