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 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.