If you decide to have a referendum, you won't lose. You hand the problem to the people. You say, here's the best we can do, or here's the best a committee of Parliament can do, now you tell us. You can't lose on that one.
You can lose if you say this is what we—our political party—want to do, and make it a political issue. You can really lose on that one.
Why lose when you don't have to? Punt the ball to the people, who really deserve to carry it.