NO REPUBLICAN in more than 60 years has governed Massachusetts for two full terms. Charlie Baker has been pretty clear about what he plans to do with the next four years, but far less forthcoming on how exactly he’s going to accomplish it.

GOP governors William Weld, Paul Cellucci, and Mitt Romney all felt the pull of ambition and either cut short their second terms or opted not to seek one. That seems unlikely for Baker, given the state of the national Republican Party – picture the unlikely scenario of a social liberal from Massachusetts stumping for GOP votes in Indiana or Alabama – and the distance he’s put between himself and Donald Trump.

Baker’s lopsided victory was the most stunning GOP win since Weld crushed Democrat Mark Roosevelt in 1994. His 67-33 takedown of Democrat Jay Gonzalez – during a great night for the state’s Democrats – means that Baker has the time and the support to push forward an agenda that will carry through 2022.

Interestingly, Baker’s number one priority could also be reminiscent of Weld – a dramatic rescue plan for the state’s worst-performing public schools. But he also faces a laundry list of expensive problems, from the failing MBTA and unaffordable housing, to the ongoing opiate crisis.

First is the budgetary problem. Like Weld, Baker says he is going to tackle the state’s toughest issues without the benefit of dollars from new taxes, something he has repeatedly said is off the table. But fixes for schools and the MBTA are going to take billions of dollars and finding that money won’t be easy – and they simply may not be possible without new taxes.

Second is the political problem. Baker is clearly personally popular. It’s just as clear that he has absolutely no political coattails. As voters gave him an enthusiastic thumbs up on Tuesday, the rest of the Republican slate went down in massive landslides. The GOP even lost ground among its anemic ranks in both houses of the Legislature. The modern conservative base doesn’t like him while the Democrats who aren’t running for governor have little reason to fear him.

Still, Baker has worked well with the Democratically-controlled Legislature. At the end of the last legislative session, it became clear that House and Senate leaders want a serious investment to close the achievement gap that separates some of the best public schools in the country – in Weston, Wellesley, Dover, and Sherborn – from some of the most challenged in many of our Gateway Cities.

Baker has repeatedly signaled that he understands the state funding formula for public schools needs a dramatic overhaul if we are going to give Brockton, New Bedford, and Worcester students greater opportunity. And he understands there may not be much choice: Brockton and Worcester are both considering lawsuits declaring the education inequity is illegal under the state constitution.

What will be fascinating over the next year is to see how Baker and the Legislature find the money to make those changes. The Massachusetts Budget and Policy Center says the cost for the Senate education bill could reach $2 billion, and even the more conservative House version would be close to $1 billion.

The MBTA fix is another area where Baker says he gets it, but has not yet identified where the funds will come from. Again, we are talking serious money: Even conservative estimates peg the need at hundreds of millions a year to make needed repairs, and the MBTA says the total cost of system renovation system is north of $7.3 billion. Critics say that number is low. Four years may not be long enough to solve that puzzle.

Like his mentor Weld, Baker faces two very big-ticket items that require deep pockets in the face of a resolve not to raise taxes. For both governors, the daunting hurdles come on the fronts of education and transportation.

Massachusetts has had no major tax increase since 2009. The T and our schools need to be fixed. Can Baker afford to risk some of his political capital with a change of heart on revenues? Or does he go the time-tested GOP route and let the Legislature pass the taxes, then override the politically popular veto?

How Baker responds is going to go a long way to determining if he keeps the title “America’s most popular governor.”

Peter Ubertaccio is dean of the Thomas and Donna May School of Arts & Sciences at Stonehill College and an associate professor of political science.