President Donald Trump is leaving office tomorrow with historically low approval ratings. Once he's gone, the Republican Party will have some soul-searching to do before they can rebuild the GOP. One name that occasionally gets talked about when it comes to the future of the Republican Party is our own Governor Charlie Baker. GBH Morning Edition host Joe Mathieu spoke with GBH News State House reporter Mike Deehan to talk more about the Massachusetts governor's impact on the GOP. The transcript below has been edited for clarity.

Joe Mathieu: So Charlie Baker [is] a moderate or even liberal Republican in an era in which the Republican Party nationally seems to want nothing to do with liberalism. We know how Donald Trump and Charlie Baker feel about each other. Does Governor Baker have much of a future in that party?

Mike Deehan: I would say yes because certainly Baker's style of politics has worked so well here, at least electorally. He's still extremely popular with Democrats [and] with Independents, less so with his own party, the Republicans. But it's working. So here voters consistently like to keep a more conservative governor to balance out the liberal legislature. So that means all signs point to a third term if Baker wants it. So Baker Republicanism is working here. Can it go elsewhere? That's kind of what the GOP needs to decide right now Post-Trump.

Watch: What is Charlie Baker's political philosophy, if we can define it?

Mathieu: Baker has said repeatedly that he doesn't like it when politicians use their current positions to get new ones. Is he even willing to be a national leader for his party?

Deehan: He says that he is willing to become a national leader within the confines of his current role as governor. One thing he says over and over again is that he hates it when politicians kind of do the stepping stone thing take one position to get to the next one. But he did actually address that last week as well, and here's what he said:

If there's some way for me to participate in broader conversations and to use the platform that this job creates for me to do that, I will do that.
Gov. Charlie Baker

Deehan: So there you have it. This is what he wants to do to exert power. But the thing is, he doesn't have a leadership role in the Republican Governors Association this year. It's unclear how he's going to be able to do that. So right now, we are kind of looking at a third term, so to speak.

Mathieu: Well, yeah, to that end, is he going to run for a third term?

Deehan: It still looks like it right now. One interesting note, he has just under $600,000 in his campaign account. His running mate, Lieutenant Governor Karyn Polito, has over $2 million. That's really the first time that it's ever been flipflopped like that. Of course, Baker can turn on the taps, fundraise [and] switch that around, they can spend the money together, but it is notable that Polito is in a position to run, should she want to.