A new survey suggests that Massachusetts could actually be a competitive Senate race heading into 2024 if Governor Baker chooses to run. Running as a Republican for Senate in a deep blue state, though, is a much different proposition than running for governor.

A statewide survey of 750 likely voters conducted by the Fiscal Alliance Foundation found that Ms. Warren would enjoy 34 percent support compared to Mr. Baker’s 49 percent. Another 17 percent reported not being sure who they would support.

“Senator Warren has significantly higher unfavorable numbers than her fellow Democrats statewide and that seems to be creating an opening for Baker, who always enjoyed large amounts of cross-party appeal,” a Fiscal Alliance Foundation spokesman, Paul Craney, said.

According to the survey, Republicans are much more supportive of Mr. Baker than Democrats are of Ms. Warren, with 79 percent of self-identified Republicans backing Mr. Baker and 56 percent of Democrats doing so for Ms. Warren.

“It’s interesting that Baker receives such solid support from Republicans, a group that he began having such trouble with during his second term,” Mr. Craney said. “Senator Warren may be doing more to unite the state Republican Party than anyone might realize.”

While this poll could be good news for Republicans aiming to win statewide elections in Massachusetts, there are a few complications.

First, the poll overrepresented independent voters and underrepresented Democratic and Republicans voters, with 37 percent of the sample being Democrats, 12 percent being Republicans, and 51 percent being independents.

According to Pew Research, voters in Massachusetts are far more partisan than this sample accounts for, with only 12 percent identifying as independents, 56 percent identifying as Democrats, and 27 percent identifying as Republicans.

Another complicating factor is that Massachusetts voters may be less eager to elect a Republican to the Senate in a year when control of that body could depend on one seat.

Ms. Warren’s seat was held by Senator Brown, a Republican, before she assumed office in 2013. Mr. Brown, however, was elected in 2010, which heavily favored Republicans following the 2008 cycle that swept President Obama into office.

The timing of Mr. Brown’s election was important because after 2008, Democrats controlled 57 Senate seats, meaning that Mr. Brown’s seat was unlikely to affect control of the body.

A political scientist at University of Massachusetts Amherst and associate director of the school’s Center for Public Opinion, John Culverius, also explains that much of Mr. Baker’s appeal is as a counterweight to national Republicans.

“The fundamental issue is that what makes Baker popular is that he is seen as a counterweight to national Republican figures,” Mr. Culverius explains. “He’s one of the few Republican governors in Democratic states that is more popular with Democrats than they are with Republicans.”

In past elections, Mr. Baker’s core constituency has been moderate Democratic voters in Massachusetts’s suburbs and exurbs, rather than Republicans in the state, who tend to be more conservative than Mr. Baker.

Mr. Culverius also explains that it would be “easy to nationalize congressional and Senate elections in Massachusetts,” particularly in a presidential election year, when turnout is typically high.

The other problem for Mr. Baker would be winning the Republican primary. According to Mr. Culverius, Mr. Baker likely decided not to seek re-election for governor last cycle because he saw that he would face long odds in a primary.

“Massachusetts Republicans are actually quite conservative and much more supportive of Donald Trump than they are of Charlie Baker,” he explains.

This phenomenon is part of the reason why popular moderate Republican governors, like Governor Scott in Vermont, Governor Hogan in Maryland, and Governor Ducey in Arizona, often fizzle out on the national stage.

The success these governors enjoy at the state level is also partially attributable to voters generally being more willing to split their ticket for gubernatorial competitions.

In Massachusetts, there is a significant portion of voters who voted for both Mr. Baker for governor and Ms. Warren for Senate in 2018.

The willingness to vote across party lines for governor is also a reason why some red states, like Kentucky and Kansas, elect Democratic governors, such as Governors Beshear and Kelly.