The findings by Education Next, a journal published by Harvard's Kennedy School and Stanford University, come as Education Secretary Betsy DeVos promotes alternatives to traditional public schools.
Forty-four percent of respondents in the poll conducted in May said they support the expansion of charter schools, compared to 39 percent in 2017. The gain of 5 percentage points, however, did not fully offset the drop in support from 51 percent in 2016.
When broken down according to party affiliation, 57 percent of Republicans and 36 percent of Democrats voiced support for charter schools, compared to 47 percent of Republicans and 34 percent of Democrats in 2017.
"Support is up among Republicans for various strategies to expand school choice, and the Trump administration's embrace of those policies is a likely explanation," said Martin West, associate professor of education at Harvard University and a co-author of the report.
Some experts noted that the issue of charter schools has become extremely politicized.
"I hate to see an issue turn into a partisan question," said Robin Lake, director of the Center on Reinventing Public Education. "I don't think that an education policy that's designed to get better outcomes for kids should ever be a partisan issue."
Support for publicly funded vouchers given to low-income families to help them pay tuition at private school rose from 37 percent to 42 percent over the past year.
Meanwhile, Americans seem to be more satisfied with their local police and the post office than with their neighborhood school. While 51 percent of respondents said they would give their local schools a grade of A or B, 68 percent gave the local post office a similar grade and 69 percent the local police.
"It makes sense that only 50 percent of Americans are giving their public school a good grade of an A or a B that they would express support for alternatives to those public schools," said Patrick McGuinn, a professor of political science and education at Drew University.
The Education Department did not immediately respond to an e-mail seeking comment.
In the Black Lives Matter era, African-American respondents gave their local police much lower marks than other respondents, but their views of their local schools were even worse. Thirty-nine percent gave their local schools an A or a B, while the local police force received such marks from 43 percent of African-American respondents.
The study also found that many Americans favor raising teacher salaries and increasing school funding in the aftermath of teachers walking out of schools in six states earlier this spring to protest pay and other issues.
Informed about average teacher earnings in their state, nearly half said they support raising teacher pay. That number was 67 percent when respondents were not told explicitly how much their local teachers were making. Nationally, the average teacher's salary was $58,950 in 2017, according to the National Center for Education Statistics.
"The sense of economic insecurity for teachers is very strong and there is growing support for higher pay, not just from teachers but from the broader community," said Evan Stone, CEO of Educators For Excellence, a teachers' advocacy organization.
West said that while many believe teachers should be making more, there is disagreement over whether they should be compensated based on how much their students learn or using some other metric.
"To the extent that the debate moves from how much are teachers are paid to how they are paid, there is potential for continued conflict," West said.
The Education Next survey was based on interviews with 4,601 adults across the country. The margin of error was 1.4 percentage points.