Republicans are so desperate to hold onto the house seat in Georgia's 6th congressional district that they are sending unpopular House Speaker Paul Ryan to campaign for GOP candidate Karen Handel.
The nearest Republican - former state secretary of state Karen Handel - came in at just 19.8 per cent.
Having Trump in the race would likely be welcomed by Democrats, who have energized volunteers on behalf of Ossoff due to their disdain for the president.
An Ossoff win would not tip the balance of power in Washington, where Republicans control the White House and both chambers of Congress.
"We defied the odds and shattered expectations - and we are ready to fight on and win in June. Onward to victory", Ossoff, a documentary filmmaker and former congressional aide who campaigned on the idea he would be a check against Trump, said Wednesday on Twitter.
Ossoff was quick to declare "a victory for the ages" for Democrats. But Trump, his political brand at stake, painted an opposing picture.
"Dems failed in Kansas and are now failing in Georgia", Trump tweeted Wednesday morning.
Ossoff will face Republican candidate Karen Handel in a runoff election in June.
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"First of all, Georgia's Sixth Congressional District - the fact that Jon Ossoff pulled in five or six points more than most Republicans thought that he would have, and Lindsey Graham said this is a wakeup call to the Republican Party, that there's a lot of moderates that need to emerge in the South to a greater degree that the Republican Party needs to pay attention to", a reporter said. "They came up short".
Spicer left open the possibility that Trump campaigns in Georgia ahead of the run-off.
In response, Ossoff portrayed Trump, a NY businessman who had never held public office, as the Washington insider.
Mr Price had won the seat in the 2016 election by a margin of 23 points - something Mr Ossoff, a political neophyte hopes he can turn around in the run-off against Ms Handel. "The progressive energy out there is palpable". If she can't, then Ossoff has a chance of winning in June.
"The reason is clear: voters are rejecting Trump and his policies". "I think we did pretty well in November, and we continue to pick up seats around the country at different levels, so I feel very confident about the state of the party", he said.
The move by Ryan - one of the most powerful Republicans in government - to insert himself into a special election in a GOP district speaks volumes about how anxious Republicans are about this race.
"It does tell you this is the kind of seat that Democrats would and should focus on", he told CNN.
But he fell short of the 50 per cent of votes needed to send him straight to Washington.