Maryland Democrats are hoping voters are so dismayed by what is happening across the border in the District of Columbia that they will take it out on Gov. Larry Hogan in this year’s elections.

Mr. Hogan is among the most popular governors in the country despite being a Republican in deep-blue Maryland, and Democrats are desperate to try to ruin the relationship. One of their chief weapons is President Trump.

In one line of attack, Democrats are demanding that Mr. Hogan take a stand on Mr. Trump’s nominee for the U.S. Supreme Court and say the fate of abortion rights hangs on the next justice.

Democrats also have accused Mr. Hogan of joining Mr. Trump to undermine the legitimacy of the special counsel’s investigation into Russian meddling in the 2016 presidential election.

Mr. Hogan said those issues aren’t relevant to his job, and voters so far seem to be OK with that.

“Sticking Trump to Hogan has really just not worked,” said Todd Eberly, a political science professor at St. Mary’s College of Maryland.

The governor’s approval rating is approaching 70 percent in some polls, and even polling commissioned by Democratic gubernatorial nominee Ben Jealous shows Mr. Hogan ahead 49 percent to 40 percent.

That is all the more stunning in a state where Democrats outnumber Republicans 2-1.

Analysts say Mr. Hogan has managed to escape the Trump trap. Many voters dissatisfied with Washington like how things are going in Maryland.

“If you’re a standard Democrat and you watch Larry Hogan, your blood pressure’s going to remain normal,” said Richard Vatz, a rhetoric and communication professor at Towson University in Baltimore County.

Given that, Democrats may feel they have little choice but to go with an approach of guilt by association.

In an interview last month, Mr. Jealous name-checked Education Secretary Betsy DeVos, Environmental Protection Agency Administrator Scott Pruitt and Attorney General Jeff Sessions as reasons to vote against Mr. Hogan.

Mr. Jealous said Mr. Hogan, “more than any other Republican,” could have blocked the appointment last year of the scandal-plagued Mr. Pruitt, who ultimately resigned last month.

“But he stood silent,” Mr. Jealous said. “All he had to do was say, ‘Hey, guys, I’m governor of Maryland, I’m [one of] the most popular governors in the country. This dude’s from Oklahoma, and he’s already promised to destroy the Chesapeake Bay restoration plan.’ “

Mr. Jealous said his path to victory in the fall is turning out a massive number of Democratic voters who stayed home in 2014 and campaigning aggressively on left-wing policy positions such as Medicare for all, free college tuition and marijuana legalization.

Still, it’s disdain for Mr. Trump that Jealous campaign adviser Kevin Harris calls the “No. 1 issue” driving many voters.

“It matters to them where their governor stands, and if Larry Hogan isn’t willing to take strong positions or adequately stand up for their values, then they’ll remember that when they vote,” Mr. Harris said.

The campaign’s recent internal poll showed that nearly two-thirds of all voters said it is “very important” to elect a governor this year who is independent of Mr. Trump and who will stand up to him if necessary.

Mr. Vatz called those persistent attempts to tie Mr. Hogan to the president “sad” and “desperate.”

“I think it’s an implicit admission that there are no seminal issues on which the Maryland electorate should be moved to vote for Ben Jealous,” he said.

The Hogan campaign says the governor is comfortable focusing on state issues and labels Mr. Jealous the candidate for “out-of-state money, out-of-state endorsements and out-of-mainstream ideas.”

“Gov. Hogan is focused on his job governing the state of Maryland, where he’s providing bipartisan leadership and getting good things accomplished on education, public safety, transportation, the environment, and health care for the people of our state,” said Hogan campaign spokesman Scott Sloofman.

The Jealous campaign says it plans to appeal to voters who say they don’t feel better off today in those areas than they did when Mr. Hogan took office.

“So we are signaling, ‘Hey, Donald Trump’s doing bad things in Washington but up here in Maryland we can be a model for how the future can actually be better for our families,’ ” campaign spokeswoman Jerusalem Demsas said. “So you’re able to combine that message in a way that pushes your base forward because it electrifies them and reminds them about Donald Trump, but it still resonates with voters who are primarily concerned with education or health care or the economy.”

The poll that showed Mr. Hogan leading Mr. Jealous by 9 percentage points in a trial heat also narrowed to a 2-percentage-point edge for the incumbent after respondents were read more specific descriptions of the candidates and their platforms.

The Hogan campaign, though, says it is telling that the Jealous campaign’s own numbers show the challenger lagging in a heavily Democratic state.

“Any way you slice the numbers, it is clear that Democrats and independents are fleeing Jealous because of his reckless and irresponsible plans to hike taxes on every single man, woman and child in Maryland,” Mr. Sloofman said.

Mr. Hogan — who didn’t attend the 2016 Republican National Convention that nominated Mr. Trump — said he has shown that he will buck the administration when he feels it’s necessary.

He was one of the first Republican governors to pull National Guard troops from the U.S.-Mexico border in the wake of the recent child separation crisis stemming from the Trump administration’s “zero tolerance” immigration policy.

Asked about the pressure campaign to weigh in on Judge Brett M. Kavanaugh, Mr. Trump’s Supreme Court pick, he said in a New York Times interview that governors have “absolutely nothing to do” with the Supreme Court.

“They elected me to do a particular job: to turn around the state of Maryland,” Mr. Hogan said. “They don’t want the governor spending his entire day fooling with Washington.”

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