Buoyed by a dramatic last-minute rally by President Trump, Republican State Sen. Troy Balderson appeared to be inching closer to beating back a challenge by insurgent Democrat Danny O’Connor in Ohio's special election for a vacant House seat Tuesday.

A victory in the race for Ohio's historically conservative 12th Congressional District would deny Democrats the major upset they had sought ahead of the November midterm elections. The winner takes the seat previously held by Republican Pat Tiberi, who resigned in January to take another job.

Speaking to cheering supporters Tuesday night, Balderson said O'Connor ran a "hard race" and claimed victory. And in a tweet Tuesday night, Trump wrote that Balderson had won a "great victory during a very tough time of the year for voting."

But O'Connor has not conceded, and said in a statement released shortly before midnight that "we don't know the results quite yet."

The race remains too close to call. Balderson maintains a slim one-percentage point lead with all precincts reporting, but there are at least 3,435 provisional ballots left to be reviewed and 5,048 outstanding absentee ballots. That's enough for O'Connor to potentially pick up enough votes to force a mandatory recount.

Unofficial Ohio state election totals showed Balderson with 101,574 votes and O'Connor with 99,820 -- a mere 1,754 vote difference.

State officials said that boards of elections cannot begin counting those additional ballots until the 11th day after the election, August 18.

The mood at O'Connor's campaign headquarters at the Ohio Civil Service Employees Association in Westerville had been optimistic early Tuesday evening as results intially indicated he was significantly ahead in Ohio's 12th Congressional District. Trump won the district by 11 percentage points in 2016, and it has had a Republican representative for the last three decades.

The race was one of several key contests on Tuesday, but it has garnered outsized attention because several polls showed no real daylight between the candidates in traditionally deep-red district -- which some, including Ohio Gov. John Kasich, has said "does not bode well" for the GOP in the upcoming November midterm elections.

Also, while Kansas, Missouri, Michigan, and Washington state were holding primaries on Tuesday, only Ohio was sending someone to Congress immediately.

Despite the apparent win by Balderson, 57, on Tuesday, the candidates will square off again in less than 100 days in November's general election. But O'Connor is expected to have much less of a fighting chance -- and outside funding -- in the fall.

Trump Tuesday night predicted on Twitter that Balderson will "win BIG" in November's general election.

Late Tuesday, as it became clear Balderson had a lead with all precincts reporting, O'Connor sounded a determined but somber note in a speech at his campaign headquarters.

"This is a grassroots campaign powered by small donations and people who want the future for their community," he said. "We won’t rest; we will keep fighting through to November."

FOUR OTHER STATES HEAD TO THE POLLS ON TUESDAY -- WHAT ARE THE KEY RACES?

A state Republican party official told Fox News that officials there were "cautiously optimistic" Balderson would prevail early in the evening, citing high turnout in areas like rural Muskingum County that nearly ran out of paper ballots.

Trump may have played a significant role in the reportedly high turnout in the Ohio contest by staging a freewheeling rally in suburban Columbus on Saturday night. In a sweltering auditorium, Trump said House Minority Leader Nancy Pelosi, D-Calif., "controls Danny O’Connor, whoever the hell that is."

In his tweet Tuesday night, Trump wrote, "When I decided to go to Ohio for Troy Balderson, he was down in early voting 64 to 36. That was not good. After my speech on Saturday night, there was a big turn for the better."

Described by campaign operatives as a "Whole Foods" district, the largely suburban region features a more affluent and educated voter base than the typical Trump stronghold.

Balderson touted Trump's help, saying Monday that the president "definitely brought major excitement, and they were excited to see him up here."

"We won’t rest; we will keep fighting through to November." — Democratic House candidate Danny O'Connor

Vice President Mike Pence also campaigned on Balderson's behalf, saying he has been on board with the president's agenda.

O'Connor has dominated Balderson on the local airwaves. His campaign spent $2.25 million on advertising compared to Balderson's $507,000, according to campaign tallies of ad spending. The Republican campaign arm and its allied super PAC were forced to pick up the slack, spending more than $4 million between them.

Kasich, a leading voice in the GOP's shrinking anti-Trump wing, once represented the district in Congress.

At times, the race has centered on Trump's tax cuts as much as the candidates. O'Connor and his Democratic allies have railed against the tax plan, casting it as a giveaway for the rich that exacerbates federal deficits and threatens Medicare and Social Security.

Democrats have also hammered Balderson for telling a local newspaper that he would consider raising the eligibility age for Medicare and Social Security.

Fox News' Kristin Fisher and The Associated Press contributed to this report.