A tough nut or a hard nut to crack is a situation, person, group, etc. which is difficult to deal with; or a place or opportunity to which it is difficult to gain entry. [wiktionary.org]

Phrases.com has a specific origin for the phrase:

This particular expression comes from 18^th when Benjamin Franklin wrote a letter to his brother. A few colonists in US were trying to attain a French Fortress somewhere in Canada in 1745. Benjamin used the following words in the letter; “fortified towns are hard nuts to crack; and your teeth have not been accustomed to it.” However, new Englanders were able to capture the fortress and thus it was proved that there are a few nuts that are much easier to be cracked.

I found no information on when or how the phrase entered popular culture, but did discover that there are other slang uses for the word “nut.” No – not the body part you’re thinking of.

[The nuts refers to] the best possible hand — is one of those great poker terms that most players learn about soon after becoming acquainted with the game… just pronouncing the word “nuts” forces the speaker to end with a smile… pokernews.com

Such a hand would be tough to crack, or win against.

Pokernews further uses a meaning of “nuts to” listed from The Oxford English Dictionary, as “a source of pleasure or delight to one.” They suggest that meaning moved into poker, where having four aces in a game of five-card draw would most certainly be “nuts to” the player holding the hand. That seems strange to me since I think of “nuts to you” as an angry retort to someone who caused upset, perhaps a euphemism for a stronger condemnation.

“The world is your oyster” has never been a favorite expression of mine, perhaps because oysters make me violently sick. Please world, don’t be an oyster for me, even if today the phrase means “you can have anything you want.”

The phrase “first appears in Shakespeare’s play ‘The Merry Wives of Windsor’ (1600).
Falstaff: I will not lend thee a penny.
Pistol: Why, then, the world’s mine oyster,
Which I with sword will open.’ Act II, Scene II.”

The original implication of the phrase is that Pistol is going to use violent means (sword) to steal his fortune (the pearl one finds in an oyster). English.stackexchange.com

Shmoop.com says “The subtext of Pistol threatening Falstaff is gone nowadays. There is no sword or threat in our modern version. Instead, we just like to think that if we’re persistent enough, we can find those oysters with pearls anywhere in the world.”

I didn’t see any earlier citations, so the Bard wins this phrase.

I’m familiar with the phrase “born with a silver spoon in the mouth” to refer to people with rich or privileged parents. But I heard a wonderful phrase the other night on TV that sent me scurrying to search. I thought I’d be offering a newly coined phrase, but I found it is well known from a Chicago Tribune interview with Barry Switzer, December 14, 1986. Although Switzer is a football coach, this is a baseball analogy:

Some people are born on third base and go through life thinking they hit a triple. wikiquote.org

There are earlier citations:

Texas politician Jim Hightower told the Democratic National Convention at Atlanta, Georgia, on July 19, 1988, about the Republican presidential candidate, George H. W. Bush: “He is a man who was born on third base and thinks he hit a triple.” barrypopik.com

But the earliest I saw, in a slightly different form, is from 1934

A genius is one who seems a wonder because he was born on third base. barrypopik.com

Since baseball’s been played in the US since 1791, and the “New York style” game played nationally since the Civil War, it’s no surprise to find a phrase coming from this sport.

In current political discussions, this phrase refers to people’s efforts to pay all their bills with inadequate funds. World Wide Words says the exact origin is unknown.

The oldest example I can find is from Thomas Fuller’s The History of the Worthies of England of about 1661: “Worldly wealth he cared not for, desiring only to make both ends meet; and as for that little that lapped over he gave it to pious uses”, but the fact that Fuller is making a little joke using it suggests he already knew of it as a set phrase.

One suggested origin refers to columns of bookkeeping numbers where credits and debits must match, or where end-of-year numbers must balance. Another suggestion is the phrase refers to having enough fabric to complete a dress.

English Language and Usage adds the possibility that the phrase comes from ropes on a sailing ship or wearing a belt that is too short, but without any references it’s speculation.