Republican Gov. Charlie Baker’s decision not to seek a third term has sparked a scramble among potential successors in a suddenly wide-open race. And it’s raised questions about the GOP’s future in the state and whether a woman finally will break through one of the last glass ceilings in Massachusetts‘ elective politics.

Can Republicans find a way to hang on to the governor’s office — their only remaining lever of power in a state when Democrats hold every other statewide office, every seat in Congress, and overwhelming majorities in the Massachusetts House and Senate?

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And is Massachusetts, one of the nation’s most politically liberal states, finally ready to elect a woman to the corner office? Since its first governor, signer of the U.S. Constitution John Hancock, took office way back in 1780, Massachusetts has elected an unbroken string of men as governor. Only one woman has served, but on an acting basis: Lt. Gov. Jane Swift, a Republican, took over as governor in 2001 after Paul Cellucci became ambassador to Canada.

With Baker out — and Lt. Gov. Karyn Polito also taking a pass — there’s no shortage of announced and possible candidates from both parties for the gubernatorial election in 2022.

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On the Democratic side, three candidates jumped into the running even before Baker’s announcement. They include Harvard professor Danielle Allen, state Sen. Sonia Chang-Diaz and former state Sen. Ben Downing.

But many political eyes are on bigger names who have yet to rule out a run, including former Boston mayor and current U.S. Labor Secretary Marty Walsh and state Attorney General Maura Healey, who has become a national leader in the legal push to hold companies and individuals accountable for the U.S. opioid addiction and overdose epidemic. Fellow Democratic Boston City Councilor Annissa Essaibi George, fresh off a defeat in her campaign to become Boston’s next mayor, is also weighing a run.

On the Republican side, the situation is equally in flux.

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While Baker remains popular in Massachusetts — including with Democratic and independent voters — he’s less popular among conservative leaders of his party and has clashed with current Massachusetts Republican Party Chair Jim Lyons, a staunch Donald Trump supporter.

Baker opted not to support Trump — or even vote for him — in the 2016 and 2020 elections. He said he decided not to run again for governor to instead focus on the state’s ongoing coronavirus response.

“There is a ton of work that’s left to be done,” Baker said.

Lyons welcomed Baker’s impending departure.

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“It’s clear to me that Charlie Baker was shaken by President Trump’s endorsement of another Republican candidate in Geoff Diehl,” Lyons said in a statement after Baker’s announcement. Trump also issued a statement calling Baker “bad news for the Republican Party.”

Diehl, a former GOP state representative from Whitman who launched an unsuccessful challenge to Democratic U.S. Sen. Elizabeth Warren in 2018, announced in July he would seek the party’s nomination for governor. Diehl is a Trump supporter who served as co-chair of Trump’s Massachusetts 2016 presidential campaign.

While Trump’s endorsement may help Diehl with Republican primary voters, it could be a political albatross in a general election in a state that twice rejected Trump by double-digit margins.

Other potential GOP gubernatorial candidates include former U.S. Attorney for Massachusetts Andrew Lelling — who led the college admissions investigation dubbed Operation Varsity Blues — Taunton Mayor Shaunna O’Connell, and Shiva Ayyadurai, who last year lost a Republican nomination bid for the U.S. Senate.

One of the top potential candidates on the Democratic side is Healey, who twice won statewide elections for attorney general. Healey, with more than $3.3 million in her campaign account, could be a formidable candidate. A fierce Trump critic, she has said she’s considering a run.

As attorney general, however, Healey faces a quirky hurdle in Massachusetts — the so-called “curse of the attorney general.” Since 1958, six former Massachusetts attorneys general have sought the governor’s office. All failed, either by losing their party’s primary, losing the general election, or in one case dying before Election Day.

Healey would face another challenge shared with other potential Democratic candidates. Again, despite their liberal reputation, Massachusetts voters like to elect Republican governors.

Of the past five elected governors, four were Republicans, going back to the election of former GOP Gov. William Weld in 1990.

Another possible Democratic candidate, Walsh, would also begin the campaign with wide name recognition and a hefty $5.1 million left in his campaign account. Walsh gained attention regionally as he shepherded the city through the first year of the pandemic. Unlike Healey, however, Walsh hasn’t run a statewide campaign.

Another name that inevitably surfaces in Massachusetts is that of a Kennedy — in this case, former U.S. Rep. Joseph Kennedy III, who last year launched an unsuccessful bid to unseat fellow Democratic U.S. Sen. Edward Markey.

Kennedy hasn’t indicated that he’s interested in running for governor.

The state has made some belated progress in electing women to top political offices.

In 2012, Massachusetts elected its first woman to the U.S. Senate when Warren filled the seat formerly held by the late Sen. Edward Kennedy. And just last month, Boston tapped Michelle Wu as the first woman and first Asian American elected to the mayor’s office.