Which is the correct idiom: "First thing's first" or "First things first"?

The correct form of the idiom is:

first things first

Things is plural here. You could imagine having a put before the idiom:

• put first things first
• let's put first things first
• you should put first things first

This clarifies the plurality of things. So, her thinking is actually fact!

The latter is generally considered correct. From Oxford Dictionaries Online:

first things first
Used to assert that important matters should be dealt with before other things.

Comparing Google hits as a very rough measure of usage gives

• "first things first": 1,660,000
• "first thing's first": 199,000

So, the apostrophised version is an order of magnitude less common, but not negligible. Interestingly (perhaps surprisingly), it appears not just in amateur but also in professional sources, e.g. Forbes.com.

The British National Corpus has 31 instances for "First things first" and none for "First thing's first". I guess the full formula is/was "Let's do first things first" and not: First thing is first, which is as illogical as "Second thing is second"- or you could call it a tautology expressing the same idea twice.

http://bnc.bl.uk/saraWeb.php?qy=First+things+first&mysubmit=Go

http://bnc.bl.uk/saraWeb.php?qy=First+thing%27s+first&mysubmit=Go