Ross Martin, who will join the SCDI from the Centre for Scottish Public Policy next month, said the gravity of next September's referendum "necessarily" means it is occupying people's minds.
But the former teacher and education convenor of West Lothian Council said there was a risk the debate may detract attention from the economic challenge.
Mr Martin said: "There is always that danger. It is a big decision whichever way people look at that decision and whatever side of the debate they may be [on].
"But underneath all that there is the nitty-gritty stuff. Life goes on and people need to maintain their focus on the day to day, and ensure decisions that are being taken, almost regardless of the outcome, support [a] strong economy, sustainability and growth."
Mr Martin said he was "cautiously optimistic" about the recovery on the basis of recent economic data but insisted "the evidence is too weak to make a judgement".
He said: "Given the scale of the crash it is too early to say whether we are climbing back out of that or not. Broadly speaking [I am] cautiously optimistic, but there is obviously an awful lot of work still to be done and therefore the need to maintain that absolute focus on the economy [is vital]. Without a strong economy not much else is possible."
Mr Martin said the diversity of the SCDI's membership was a major strength. He said a key priority would be to find common ground between members, while preserving the SCDI's reputation as "an honest broker - a place for mature, reflective discussion".