Democratic and Republican leaders dueled on Wednesday over GOP gubernatorial candidate Charles D. Baker’s role in shaping the Big Dig financing mechanism, as Baker’s entrance into the race quickened the pulse of the gubernatorial campaign.

State Democratic Party chairman John Walsh retooled a line of attack that Governor Deval L. Patrick’s campaign used against Baker in 2010, laying the blame for the Big Dig’s explosive pricetag at the feet of the former state budget chief.

“One of the biggest problems that confronted Massachusetts during his time, when he was responsible for our finances, were the cost overruns and the late progress of the Big Dig,” Walsh said during a press conference at Democratic headquarters. “We now know from the last campaign that Charlie Baker was the author of the Big Dig financing plan.”

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Former Governor William F. Weld, for whom Baker worked as a health care and finance aide, said that Baker had not been the plan’s chief author.

Weld said Baker was “definitely not the point person” on the project. Instead, Weld said, the “point person” had been Paul Cellucci, who first served as Weld’s lieutenant governor and later governor in his own right. Cellucci died in June.

Much of Baker’s part in the Big Dig was litigated during the 2010 campaign, when Democrats dubbed him “Big Dig” Baker and tried to press him on a 1998 memo he wrote to Cellucci warning of the project’s “simply amazing” costs.

Walsh, speaking at a press conference at party headquarters, said the issue would be freshly relevant in the 2014 campaign, calling it “the most dominant thing” in Baker’s record.

Speaking with reporters shortly later on the Greenway, Weld drily noted that the massive transportation project had been “on time and on budget” when he left office, and said the problems came later.

Weld, who encouraged Baker to run again, said he expected a looser candidate in his second bid.

“He’s the best candidate any party could put up in any state,” Weld said.