Say I have 2 influence and want the shotgun which is 4 successes. If I roll 2 successes, can I spend 2 clue tokens to reroll my success to attempt to get the shotgun or does rerolling a die remove that success and in theory I wouldn't be able to get the shotgun with my default influence and without a loan?
You only count successes once all rerolls have been made. This can be inferred from this clause in the rulebook:
Immediately after rolling dice during a test, an investigator may spend a Clue token to reroll one die. He may perform this multiple times, as long as he spends a Clue token each time. He determines whether he passed or failed after resolving all rerolls.
Also, in the reference guide, you'll find:
When a die is rerolled, use the result of the reroll, even if the new result is worse.
So, clearly a reroll can remove a success if that dice is rerolled! This makes it entirely clear you are just manipulating the result of a roll of a fixed number of dice. You can never get more successes than the original number of dice in the pool.
This becomes even clearer when you remember that there are effects that allow an investigator to roll additional dice. If the intent was to allow rerolls to create additional successes, there wouldn't have been any need for the additional dice mechanic.
Successes and failures are only counted after you finish rerolling.