The two races will garner the most national attention on a day when four states hold primary elections: Kansas, Michigan, Missouri and Washington.
The August election was to fill former GOP Rep.
OH polls closed at 7:30 p.m., but the counting could take hours more.
Balderson leads O'Connor, 50.1% to 49.3%, with 99% of precincts reporting, according to the Associated Press Provisional ballots remain to be counted, and it's possible the race could be headed to an automatic recount, which is triggered when the margin is within 0.5%.
Republicans are scrambling to avoid an embarrassing defeat in a seat that the party has held for decades.
Trump visited Ohio's 12th District on Saturday and appeared on stage with Balderson at a rally created to jolt conservatives into turning out to vote in an election that will gauge where the Republican Party stands less than three months before the midterms.
"I've worked in OH presidential and senate races for Republicans and the idea of #oh12 being a close race is sort of like hearing gravity is a regional phenomena", tweeted Republican strategist Stuart Stevens. "If the GOP can't hold this district, which last elected a Democrat back in 1980, then it's a pretty safe bet Democrats will recapture the House in November", King continued.
CNN chief national correspondent and anchor John King on Tuesday noted that a Democratic win in Tuesday's special election in a heavily-red district in OH could signal a blue wave in the fall that would likely put impeachment "on the table".
Strategists in both parties admit that both candidates were fairly mediocre, making the OH race essentially a test of a generic Democrat versus Republican that didn't have as many local vagaries as some other special elections.
It's unclear how much Trump's support helped or hurt Balderson.
Kansas Republicans were fighting among themselves in a battle for governor, where Secretary of State Kris Kobach was trying to unseat Gov. Jeff Colyer.
Democrats, meanwhile, have been attacking Balderson by casting his support of tax cuts as threats to Social Security and Medicare.
Trump made his preference clear for Kobach. Strong on Crime, Border & Military.
The five-way Democratic primary featured labor lawyer Brent Welder, who campaigned recently with self-described democratic socialists Vermont Sen.
After Alexandria Ocasio-Cortez's stunning victory in NY against Rep. Joe Crowley, progressives hope to demonstrate that their policies can win over voters in the middle of the country.
O'Connor has dominated Balderson on the local airwaves.
Missouri Attorney General Josh Hawley is expected to take on McCaskill, and in MI, military veteran and business executive John James is vying for the chance to knock off Stabenow.