Having been swept aside by Wales in their RBS 6 Nations Championship opener at the Millennium Stadium last week, it would be difficult to find even a Scot who would back them to beat the world champions at Murrayfield this weekend.
But the optimistic Australian has issued a passionate rallying call in the capital and genuinely believes his new-look team could shock England.
Williams said: "We're really looking forward to it and we're going to take it on.
"Every Scottish supporter leaving the ground on Saturday will know that we have give every drop of desire, passion, sweat and blood, if necessary, to win the game.
"The English are world champions but of course I believe it. If I didn't believe it I would get out of here.
"They (Scotland) are a fine young team and great young men to work with. They are trying their hearts out.
"There is always the opportunity to win but the odds are stacked against us.
"You've got to respect your opponent but not pay them too much respect.
"We will continue to fight for the 80 minutes and we will not be intimidated."
Williams has named two changes in his side to take on Sir Clive Woodward's team.
Following their dismal defeat in Cardiff last week, he has promoted Edinburgh's centre/wing Simon Webster and Sale Sharks' lock/back-row forward Jason White to his starting 15.
Edinburgh's Allister Hogg, who made his debut against Wales, and Glasgow's Andrew Henderson have made way.
Scotland team to play England in the RBS 6 Nations Championship on Saturday 21 February at Murrayfield.
Ben Hinshelwood (Worcester); Simon Danielli (Bath), Tom Philip (Edinburgh), Brendan Laney (Edinburgh), Simon Webster (Edinburgh); Chris Paterson (Edinburgh, captain), Chris Cusiter (The Borders); Tom Smith (Northampton), Gordon Bulloch (Glasgow, vice captain), Bruce Douglas (The Borders), Scott Murray (Edinburgh), Stuart Grimes (Newcastle Falcons), Jason White (Sale Sharks), Simon Taylor (Edinburgh), Cameron Mather (Glasgow)
Substitutes: Robert Russell (Saracens), Gavin Kerr (Leeds). Nathan Hines (Edinburgh), Allister Hogg (Edinburgh), Mike Blair (Edinburgh), Dan Parks (Glasgow), Andrew Henderson (Glasgow)