A judgment on Mr McKinnon is expected within three weeks
Extraditing a Briton accused of the "biggest military computer hack of all time" to the US would be an abuse of proceedings, the law lords have heard.
Lawyers for Glasgow-born Gary McKinnon told the House of Lords US authorities had warned him he faced a long jail sentence if he did not plead guilty.
The systems analyst is accused of gaining access to 97 US military and Nasa computers from his London home.
Known as Solo, he was arrested in 2002 but never charged in the UK.
John Reid, home secretary at the time, granted the US extradition request.
His lawyers told London's High Court last year that he was subject to improper threats and extradition would breach his human rights.
Two judges found no grounds for appeal.
At the House of Lords on Monday, David Pannick QC, representing Mr McKinnon, said US authorities had warned his client he faced a life sentence rather than a couple of years in jail unless he agreed to plead guilty and to extradition.
Without co-operation, the case could be treated as a terrorism case, which could result in up to a 60-year sentence in a maximum security prison should he be found guilty on all six indictments.
With co-operation, he would receive a lesser sentence of 37 to 46 months, be repatriated to the UK, where he could be released on parole and charges of "significantly damaging national security" would be dropped.
A US embassy legal official quoted New Jersey authorities saying they wanted to see him "fry".
Mr Pannick said it was not disputed that the courts could refuse to extradite people if they considered there had been an abuse of process.
Mr McKinnon has never denied accessing the computer networks between February 2001 and March 2002.
He said he was motivated by curiosity and only managed to get into the networks because of lax security.
Clare Montgomery QC, representing the Home Secretary, argues no threats were made, and the extradition should go ahead.
Judgment is expected within three weeks.