Speaking outside the High Court, Ms Sharp said President Obama should help those campaigning on her son's behalf make the world "a more compassionate place".
"Obama wouldn't have this. He doesn't want the first guy extradited for computer misuse to be a guy with Asperger's [Syndrome], a UFO guy.
"I'm just praying, please hear us, Obama, because I know you would do the right thing," she added.
Glasgow-born Mr McKinnon admits hacking by accessing 97 government computers belonging to organisations such as the US Navy and Nasa, but denies it was malicious. He also denies the allegation he caused damage costing $800,000 (£487,000).
He has always insisted he was looking for classified documents on UFOs, which he believed the US authorities had suppressed.
Supreme Court challenge
Mr McKinnon has challenged refusals by the home secretary and the director of public prosecutions (DPP) to try him in the UK.
But the DPP refused to order a UK trial, saying the bulk of the evidence was located in the US and Mr McKinnon's actions were directed against the US military infrastructure.
Gary McKinnon suffers from Asperger's Syndrome
Mr McKinnon could face 60 years or more in prison if convicted in the US.
Whether or not he can appeal to the new UK Supreme Court - due to launch in October - will be decided later, Lord Justice Burnton, one of two High Court judges to hear his case, said earlier.
The two judges ruled extradition was "a lawful and proportionate response" to his offence, even though they conceded he might find extradition and prison in the US "very difficult indeed".
Mr McKinnon's lawyers argued extradition was "unnecessary, avoidable and disproportionate".
Karen Todner said her client was "clearly not equipped" to deal with the American penal system.
'Out to dry'
Tory leader David Cameron said the case raised "serious questions" about the extradition pact between the US and UK.
"Gary McKinnon is a vulnerable young man and I see no compassion in sending him thousands of miles away from his home and loved ones to face trial."
US-UK EXTRADITION TREATY
2003 treaty, agreed in aftermath of 9/11 attacks
Offence must be punishable by one year or more in jail in both countries
US has to prove "reasonable suspicion" for extradition of a British citizen
To extradite an American from the US, British must prove "probable cause"
Since 2004, 46 people have been sent from the UK to the US for trial, and 27 from US to UK
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