The former Kilmarnock, Hibs, Plymouth and Chester manager was unveiled earlier this week as the surprise successor to current Hearts manager Csaba Laszlo as coach of Uganda.
The Cranes will qualify for both the next stage of the World Cup qualifiers and the African Cup of Nations for the first time in 30 years if they succeed in winning their next two games, away to Niger and at home to Benin.
And the former Rangers striker has been told by the Uganda FA (Fufa] that his long-term future hinges on qualification being accomplished.
Fufa president Lawrence Mulindwa said: "Williamson has a short-term contract with Fufa. If we are satisfied with his work, then we shall sign a long-term deal.
"As Bobby can see, our media want results. We need six points from the two remaining matches to progress. If he takes us there, he will be our hero."
Former Rangers striker Williamson insisted the pressure didn't faze him. He said: "There is a lot expected of me and I'm determined to deliver. This is a big honour for me.
"There will be pressure on my shoulders, but I have learnt how to deal with it and aim to combat it."
Williamson, who will make his Ugandan bow next month in Niamey's General Seyni Kountche Stadium, described how an interview in the country's capital, Kampala, had sealed the post for him. "The job became available, I applied for it and got it," he said.
"I will now give it 100 per cent as I have done with every job I had."
Williamson's managerial career started with what has proved to be the highlight so far, winning the 1997 Scottish Cup with Kilmarnock. After also guiding the Rugby Park club to Europe, Williamson was lured to Hibs, but although he took them to the CIS Cup final in 2004, he often had a strained relationship with supporters, and departed towards the end of that season.
Williamson took the reins from Paul Sturrock of a Plymouth side already on course for the League One title but was sacked early in the 2005/2006 season after a poor run of results. A ten-month stint as manager of Chester City was his last permanent post before Uganda hired him.
He added: "I think it goes to show that football is my life, this is my career and it's what I do.
"I just want to be involved in football. I still feel I have something to offer and thankfully they feel the same way. All I can do now is give it my best."
Williamson knows he can quickly secure hero status if he guides his new charges through their two crucial qualifiers.
Uganda last qualified for the Africa Cup of Nations in 1978, when they reached the final before losing 2-0 to hosts Ghana.
To take them back to the finals would guarantee him adulation, as would a step closer to the World Cup in South Africa in 2010.