They both mean that the object will soon be reached. Literally, a few steps will take you to the house "round the corner." Figuratively, the passing of a few days (or weeks or months, whatever the context) will take all of us to the election "round the corner."
[you and a friend are working on a project]
"I think we should use a bigger piece of posterboard and a red marker."
"Okay, I'll run out and buy some. I won't be long, there's a shop right around the corner. I'll be right back."
[the project is making posters for your candidate]
"These posters look great."
"Yes, but we'll need lots more. Let's try to work on them every night this week---you know, the election is right around the corner. It will be here before we know it."
[native speaker, not a teacher]