「～っこない」 is an expression that means "there's no way one could ..."
The sentence in your question means "you may think of that, but there is no way you could do it actually."
Here are some more examples:
「そんなの食べられっこない」 (taberarekkonai) = there's no way I could eat that stuff.
「月末に間に合いっこない」 (maniaikkonai) = there's no way I'd make it by the end of this month.
「ばれっこないって」 (barekkonai) = I bet nobody would notice.