Mark Donnelly, 23, from Greencastle, denies killing the 19-year-old from Tydavnet, County Monaghan in 2012.
Mr McGovern died after being punched during a night out in Omagh, County Tyrone, on New Year's Eve in 2012.
Jurors will return to Dungannon Crown Court on Friday to resume their deliberations.
In his closing speech to the jury, a prosecution lawyer said Mr Donnelly was either a "cowardly liar" or the "unluckiest man alive".
However, a defence lawyer said evidence from a key witness identifying Mr Donnelly as the attacker was "a catalogue of errors" and "mistaken in a number of key respects".
The judge told jurors the key issue was the question: "Did the defendant strike the blow in the Weigh Inn car park?"
The prosecution lawyer said Mr McGovern, despite "extreme provocationâ€¦ did his best to defuse a volatile situation".
He said Mr Donnelly was "a man who would do anything to save his own skin" and had attempted to "hoodwink" and "pull the wool" over the eyes of the jury.
He claimed the defendant was responsible for both a "cowardly punch" and a "cowardly denial" and he was "not brave enough to admit" what he had done.
The prosecutor said if Mr Donnelly was innocent, he was a "very unlucky man" in being identified by a witness, and being filmed on CCTV in the area seconds before and after the assault.
He told the jury: "Because the (CCTV) camera doesn't show him hitting Jason McGovern he's thinking he's going to fool you into thinking he didn't throw the punch. It's just a charade."
He added: "You may think he is the unluckiest man alive or he is guilty. I say there is no doubt about that. Mark Donnelly is guilty of manslaughter. Mark Donnelly is guilty of punching Jason McGovern."
In summing up the defence case, a lawyer told the jury that there were "too many problems with the evidence of (the key prosecution witness) for you to be satisfied beyond reasonable doubt of the guilt of this young man".
He said the witness had admitted that she could have made a mistake and pointed to the evidence in the witness box of Mr Donnelly, who had said: "I say that she is mistaken. I did not strike anyone down by the Weigh Inn car park."
He said even if the jury took the view that Mr Donnelly had been lying, the jury "must not assume for that reason the defendant is guilty of the offence of manslaughter".
The judge told the jury that the death of Mr McGovern was "very emotive", but they must approach their task "quite clinically".

The site, on Newington Causeway near Elephant and Castle, will contain 38 flats and three floors of shops.
Southwark Council's planners approved the scheme by four votes to three.
The club said it was "extremely disappointed" and thought the decision was "wrong".
It had fought the proposals, fearing people moving into the flats could submit complaints about noise levels which might lead to the venue closing.
The council said the new block was in "a prime location" in central London and part of the regeneration area around Elephant and Castle.
"Any improvement to this area would be of great benefit to local people," said Councillor Fiona Colley, the borough's cabinet member for regeneration.
"We appreciate that the Ministry of Sound is a valued club, business and local employer which we have no intention of seeing close.
"I believe the club can and will remain open alongside new residential developments," she added.
But Lohan Presencer, the venue's chief executive, said his firm was taking legal advice "and will be doing everything we can to prevent this catastrophic threat to the future of our business".
"We believe that the council has mishandled this application, failed to understand or acknowledge its implications at every turn and that they have now misdirected their councillors to the wrong decision," he said.
The club collected 25,000 signatures when opposing the previous development, which proposed 315 homes on the same street.
The musician Example was among those speaking out about the proposal, which the council rejected on the grounds of noise and as it did not meet requirements for affordable housing.
The jury in the trial of a man accused of the manslaughter of Jason McGovern has been sent home for the day after hearing lawyers sum up their cases.
[NEXT_CONCEPT]
A 22-storey tower block has been approved close to the site of the Ministry of Sound nightclub in south-east London, three weeks after another development nearby was rejected.