His first match in charge was a narrow 1-0 home defeat by title-chasing Rangers, before a hugely impressive 2-1 come-from-behind victory at Falkirk.
It was their first win in six league matches and kept them above rejuvenated Kilmarnock on goal difference.
"I know how it goes," said McLeish. "If you lose those two games, I'm not in the conversation at all.
"I think we had two relatively-positive performances. Again, still so much about those that I'm not entirely happy about and want to keep improving on, but I think we've got things moving in a decent direction.
"I view it right now as I'm the guy sitting here and I need to do well enough to make sure that the club have no choice but to stick with me.
"Again, I also understand that in the football business if that doesn't happen, the club make a change, I'm absolutely comfortable with whatever happens."
Jamie Langfield, Allan McManus and Marc Kelly have been assisting McLeish and now former St Mirren defender Stuart Taylor has joined the backroom team.
That collective would appear to offer continuity.
McLeish was involved during Robinson's hugely successive tenure - three top-six finishes and this term's League Cup triumph. He knows the players and tactics already.
The general consensus from supporters seems to be positive. Continuity is perceived as a good thing given what's at stake, rather than starting from scratch under a new manager.
"I absolutely back myself and what I can do, but more importantly, I back the group of players that we've got," added McLeish.
"We've got more than enough in our dressing room to keep pulling ourselves out of this situation. We've shown what we can do.
"Massive cup semi-final game as well, where we have to go into that with every confidence in the world and our aim is to progress in that and to win as many games as we can from now until the end of the season."

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