Democrats hoping for a major upset victory in a pivotal Ohio special election Tuesday touted a new poll suggesting the House race is a virtual tie, while Republicans made an all-out final push to avert a potentially embarrassing loss in a district they have controlled for decades.

Several other states will head to the polls for key primary fights on Tuesday, including Missouri, Michigan, Kansas, and Washington. But the tight race for Ohio's wealthy and highly educated 12th Congressional District, which has had a Republican representative for more than 35 years, is seen as a particularly crucial indicator of how President Trump's progress in office could be faring with conservatives.

Tuesday's contest in Ohio is not a primary, but a special election to determine who will take the House seat held by retired Rep. Pat Tiberi. A poll conducted earlier this month by the Emerson College Polling Society and released Monday found that the upstart Democrat in the race, 31-year-old Danny O’Connor, is holding onto a one-percentage point lead over two-term Republican State Senator Troy Balderson, 56, with seven percent of very likely voters still undecided.

That's well within the poll's margin of error, and it mirrored a Monmouth University survey released last week showing no statistically significant daylight between the candidates. Trump took the district by 11 points in 2016.

During a canvassing event Monday featuring actress and Cleveland native Kathryn Hahn, O'Connor seized on the polls, urging volunteers to press on through the evening even when they're tired or thirsty for the sake of change in Washington.

"We're part of a movement," he said. "We are part of a grassroots movement that's going to change the way that politics works."

All available polls in the race were conducted prior to President Trump's freewheeling rally Saturday night in suburban Columbus, however, and Republicans are hoping that the combination of big spending and national star power will turn the tide. At the rally, Trump said House Minority Leader Nancy Pelosi, D-Calif., "controls Danny O’Connor, whoever the hell that is."

WATCH: TRUMP RIPS O'CONNOR AS 'PUPPET' FOR PELOSI IN SWELTERING RALLY

O'Connor once vowed not to vote for Pelosi to lead the party again, but later backtracked, saying he would support her if it was necessary to retake the House.

Working phones at a volunteer site Monday, Balderson said he's felt enthusiasm throughout the district following Trump's visit Saturday.

"He definitely brought major excitement, and they were excited to see him up here," Balderson said. "To stand on stage [with Trump] was incredible."

Vice President Mike Pence also has visited the state to help defend the seat, which was was held for 18 years by GOP Gov. John Kasich and nearly another 18 by Tiberi, a pro-business, establishment Republican. Both are backing and campaigning for Balderson in Tuesday's special election for the remainder of Tiberi's unexpired term.

Balderson is a Trump supporter but also has aligned himself with Kasich, an outspoken Trump critic who ran against the president in 2016.

Kasich said Sunday on ABC News' "This Week" that the close race "doesn't bode well" for Republicans, calling it a "shocking" turn of events in the GOP stronghold.

WHAT OTHER STATES ARE GOING TO THE POLLS ON TUESDAY?

Besides big names, Balderson also has the backing of big money. Independent expenditure groups have spent more than $3.7 million in the race in advertising on his behalf, more than five times what Democratic groups have contributed.

Still, Democrats have hammered Balderson for his association with Trump, as well as for telling a local newspaper that he would consider raising the age for Medicare and Social Security.

"I have no problems raising the age" for Medicare benefits, Balderson said in an interview with the Columbus Dispatch. He responded "yes" when asked if he would consider changing the rules for Social Security eligibility, as well. His attempts to soften the impact of the statements by saying he wouldn't change eligibility for retirees or those "approaching" retirement did little to deflect criticism.

"We are part of a grassroots movement that's going to change the way that politics works." — Ohio Democratic nominee Danny O'Connor

Also on Tuesday, Republicans in Missouri will pick their nominee to take on Sen. Claire McCaskill, the Democratic incumbent who is considered vulnerable in November. Out of a crowded field of Republican candidates, Missouri Attorney General Josh Hawley has emerged as a favorite, even securing Trump’s endorsement months before the primary election.

And in Kansas, Gov. Jeff Colyer is seeking his first full term leading the state, but Kansas Secretary of State Kris Kobach received a last-minute endorsement from President Trump.

Democrats need to secure an additional 23 seats to obtain a House majority in November.

Fox News' Kaitlyn Schallhorn and The Associated Press contributed to this report.