Oregon Gov. Kate Brown positioned herself early on as a leader of the anti-Trump opposition, but the state’s never-ending panoply of protest activity has backfired on her re-election bid with voters suffering from resistance fatigue.

Ms. Brown, who was expected to coast to victory in deep-blue Oregon, has found herself deadlocked in the latest polls with state Rep. Knute Buehler, an affable orthopedic surgeon whose moderate brand of Republicanism is attracting crossover voters.

That includes Ben West, who supported Ms. Brown’s previous bid for office but was horrified by the mobs that shut down the Immigration and Custom Enforcement office in Portland for five weeks, leaving behind so much trash that the area was ultimately declared a biohazard.

What stuck with Mr. West was the sight of Occupy ICE protesters scaling the building, removing the U.S. flag, and waving the Antifa flag, a display he described as “appalling.”

“It just goes to a lack of true leadership because that’s chaos. I feel like the state is in chaos. And it feels awful,” said Mr. West, executive director of Oregon Foster Families First. “It’s not the Oregon I know and grew up in.”

Mr. West, a registered nurse and fifth-generation Oregonian, isn’t what you’d call a staunch right-winger. He and Paul Rummell were plaintiffs in the state’s gay-marriage lawsuit, exchanging vows after same-sex unions were legalized and later adopting a foster child.

Instead of egging on the resistance, Ms. Brown should be grappling with Oregon’s very real problems, he said, including the growing public-pension shortfall, a child-welfare system in crisis, and the homeless encampments that have spread from downtown Portland to leafy enclaves like the Overlook neighborhood.

Since Mr. Trump was sworn in in January 2017, Portland has become ground zero for protests, including shout-downs at city council meetings, Antifa-versus-Patriot Prayer weekend slugfests, and too-many-to-count rallies and marches decrying the Trump administration over everything from guns to immigration.

Portland Mayor Ted Wheeler has taken most of the heat from both sides over the unrest, but Ms. Brown hasn’t been immune from criticism as Oregon continues to draw national headlines for its protest clashes.

“She’s had an opportunity but we’re continuing to spiral down,” said Mr. West. “The ship is sinking and the captain is nowhere to be found.”

Referendum on her record

The governor’s race comes as a rematch for the candidates, who faced off in the 2012 contest for Secretary of State. Ms. Brown won that election by 53 to 41 percent. In February 2015, she unexpectedly became governor when Gov. John Kitzhaber resigned over an ethics scandal involving his fiancée.

Ms. Brown won the 2016 special election to retain the post, becoming the first openly LGBT person—she’s been married to her husband since 1997 but has described herself as bisexual—to be elected governor in the nation.

A favorite of Planned Parenthood, LGBT groups and public-employee unions, Ms. Brown’s candidacy is still the way to bet, but a Gravis Marketing poll released July 24 shook the race by showing the candidates tied at 45 percent.

A week later, a Clout Research poll released Aug. 2 found Mr. Buehler leading by 43.1 to 41.9 percent.

The Cook Political Report downgraded the race last week from “likely Democrat” to “lean Democrat,” while political analyst Larry Sabato did the same, pointing to Ms. Brown’s “relatively weak” seven-point win in 2016.

“One would still rather be the incumbent Brown in a blue state that hasn’t elected a Republican governor since 1982, but our understanding is that the polling is close enough that an upset is possible,” said Sabato’s Crystal Ball. “We’re moving Oregon from Likely Democratic to Leans Democratic.”

Ms. Brown has swung back by touting her achievements, citing Oregon’s job growth and falling unemployment on her watch, but it’s her battles against the Trump administration that have defined her tenure.

She roused her supporters by declaring in April that she would refuse to send Oregon National Guard troops to the U.S.-Mexico border, and blasted the president’s “reign of terror” after Occupy ICE set up camp in June.

“Trump reign of terror against our communities, against our immigrant families is absolutely unacceptable and it must stop. It is causing chaos in our families, in our communities, in our businesses all around the state,” she told the Oregonian in a statement. “It’s absolutely unacceptable.”

Meanwhile, the November initiative ballot could be described as a referendum on her record. Measure 106, which would ban public funding for abortion, came after she signed a bill in August 2017 making Oregon the first state to offer free abortions for all.

Measure 105 would repeal the state’s sanctuary law for illegal immigrants, which she has defended. She signed in April a hotly contested bill that would raise taxes on small businesses; there are now two anti-tax initiatives on the ballot.

Mr. Brown may be focused on the Trump agenda, but not Mr. Buehler, who wrote in John Kasich’s name on his 2016 presidential ballot. The Republican has since said he is “concerned” about some of President Trump’s actions but has otherwise made it clear he wants to concentrate on Oregon, not the Trump administration.

That hasn’t slowed Ms. Brown’s commitment to the resistance. Last week, she took a jab at the president’s nominee for the Supreme Court, declaring at a press conference that she signed the abortion bill in part because “we knew that this was a possibility.”

“[T]hat the president has threatened to take away our very basic and fundamental rights to choose, the right to make decisions about our own bodies,” said Ms. Brown. “And we wanted to make sure that women across Oregon, regardless of their income, regardless of their zip code or where they live, were protected.”