I cannot hear difference between 'a' and 'the'! Too short sound.
Yes, sometimes everything becomes a "schwa" in fast speech -- thus the use of phonetic alphabets in radio (Alpha, Bravo, Charlie, Delta...)

Which reminds me of a little game. Below are the titles of seven famous English "сказки", respelled as they might sound when heard over a bad telephone connection. Can you match each title with its plot? (It may help to read the words aloud -- strongly-stressed syllables are underlined.)

1. Ladle Rat Rotten Hut
2. Insulin Griddle
3. Check Under Beam Stock
4. Gull Deluxe Inner Tree Pairs
5. Fruit Or Luke Ink Less
6. Free Whittle Pegs
7. To Prances Ender Bee

a. A criminal breaks into a house and destroys everything belonging to the baby.
b. Magic beans grow to giant heights.
c. A girl finds herself in a land of talking chessmen.
d. True royalty is revealed by extremely sensitive skin.
e. He who builds the strongest house is safest from the villain.
f. A cannibalistic witch traps children with candy.
g. Elderly woman turns out to be furry "drag queen."