Q:

Someone whose aspirations exceed abilities or means

What would be a clear and concise way to describe someone whose ambitions or aspirations far exceed his means or abilities?

A:

“His reach exceeds his grasp.” This comes from Robert Browning's poem 'Andrea del Sarto' which contains the lines:

Ah, but a man's reach should exceed his grasp,
  Or what's a heaven for?

A:

A person with ambitions or aspirations that far exceed their means or abilities would be quixotic. The term is a good fit because of its definition and because it brings to mind Don Quixote providing a mental picture of aspirations exceeding abilities.
quixotic

ADJECTIVE
  Extremely idealistic; unrealistic and impractical.
  ‘a vast and perhaps quixotic project’  English Oxford Living Dictionaries

In this case an example would be: "Bob has quixotic ambitions"
Etymology

Quixotic Has Roots in Literature
  If you guessed that quixotic has something to do with Don Quixote, you're absolutely right. The hero of the 17th-century Spanish novel El Ingenioso Hidalgo Don Quijote de la Mancha (by Miguel de Cervantes) didn't change the world by tilting at windmills, but he did leave a linguistic legacy in English. The adjective quixotic is based on his name and has been used to describe unrealistic idealists since at least the early 18th century.  Merriam-Webster

A:

You could work in an allusion to Thurber's character Walter Mitty.
Wikipedia explains:

Walter Mitty is a fictional character in James Thurber's first short
  story "The Secret Life of Walter Mitty", first published in The New
  Yorker on March 18, 1939, and in book form in My World and Welcome
  to It in 1942. Thurber loosely based the character, a daydreamer, on
  his friend Walter Mithoff. It was made into a film in 1947 starring
  Danny Kaye, with a remake directed by, and starring Ben Stiller
  released in 2013.The character's name has come into more general use
  to refer to an ineffectual dreamer and appears in several
  dictionaries. The American Heritage Dictionary [see also the American Heritage Dictionary of Idioms] defines 'a Walter
  Mitty' as "an ordinary often ineffectual person who indulges in
  fantastic daydreams of personal triumphs".

Examples:

He has been described as the Walter Mitty of the political world, a
  complete nobody who has somehow contrived a career out of standing on
  a soapbox and protesting against anything the mainstream politicians
  do.

...............

My father worked for the same company for over 50 years and never even
  left his home state, but he was always something of a Walter Mitty,
  dreaming about a life of adventure.

[both Farlex Dictionary of Idioms]

