BOSTON — Charlie Baker may be one of the most popular governors in the country, but critics say he has been reluctant to spend down his political capital on potentially bruising policy fights. That is, until now, with the Republican all-in on an issue he has championed throughout his public life: charter schools.

Baker has appeared in a television ad urging voters to support a ballot question to expand the number of charter schools. He has knocked on doors and chatted up voters one on one. He has even defended a member of his administration who ponied up $100,000 for the group backing the measure.

Gov. Charlie Baker

There’s no guarantee Baker will succeed. A poll released Thursday by Suffolk University and The Boston Globe found an even split, with 45 percent of those polled supporting the question and 45 percent opposed, with 9 percent undecided. Earlier polls showed the “no” vote ahead.

It’s not just charter schools. Baker is also tapping his popularity to fight a ballot question that would legalize the recreational use of marijuana in Massachusetts. Several recent polls have shown the question ahead .

The Suffolk University/Boston Globe poll also reaffirmed Baker’s popularity.

According to the survey , the Republican is seen favorably by 64 percent of likely voters and unfavorably by just 12 percent. The numbers put him just slightly behind President Obama, who remains extremely popular in Massachusetts, at 67 percent.

The poll of 500 likely voters, conducted Oct. 24-Oct. 26, has a margin of error of plus or minus 4.4 percentage points.

Baker is hoping to tap that store of goodwill to persuade voters to pass the charter school question.

In his new pro-charter school television ad, Baker makes his case, speaking directly to the camera.

“Imagine if your kids were trapped in a failing school. Public charter schools give parents a choice and are a pathway to success for these kids,” Baker said. “If you like your school, Question 2 won’t affect you, but Question 2 will change the future for thousands of kids who need your help.”

In the charter school battle, Baker is fighting back not only against teachers unions, but also local school committees and dozens of mayors who oppose the question.

It’s the kind of pitched political battle that Baker has largely avoided as he has worked to win over natural political foes in a state Legislature overwhelming dominated by Democrats.

David Paleologos, director of the Suffolk University Political Research Center in Boston, said Baker could appeal to voters still on the fence.

“This question will be decided by these undecided voters, and Gov. Charlie Baker could have an impact,” he said.

Jeffrey Berry, a professor of American politics and political behavior at Tufts University, said Baker has been “uber-cautious,” focusing on efforts to control state spending.

But Baker is going to need more than a balanced budget if he runs for re-election in 2018, Berry said.

Without spending down some of his political capital, Baker could end up without a single big achievement he could point to in his first term.

Any big achievement typically involves risk of failure, he said.

“Sticking his neck out on charter schools is the first real indication of that,” Berry said. “He runs the risk of coming out the loser.”