How long does it take to decrypt an RSA/ECB encrypted message?
This is basically a substitution cipher where words are converted to numbers and then those numbers are substituted for new numbers as the encryption step.  You'd need to assume the language of plaintext, let's assume it's English.

Every time the word "the" occurs in the original text, it will cause the same number to be output to replace it.  Using some word frequency tables, it may be possible to find patterns that occur in the cyphertext that represent common patterns in English usage.

I guess I would have to look and see if there is a technical definition for decrypt, but even if you managed to puzzle out a possible sentence by analyzing the cyphertext, does that count as a decryption if you cannot reproduce your assumed input generating the same output.

Despite this being a very bad way to use RSA, it would still not make it any easier to officially decrypt the message.  The only way to do this with absolute certainty, is to factor the primes that make up the private key.  Depending on the size of the primes involved, this is a pretty intractable problem...

As the commentor above notes... if a word won't fit into the modulus, then keysize might be pretty small.  The longest word in English is something like 28 letters, so 28*8 is 224 bits.  There is no way that antidisestablishmentarianism was what the question had in mind, so lets make an assumption that any word longer than 8 characters is one that would need to be broken up...  That would be a modulus of 64 bits.  So now, the question is, how long would it take to factor a 64 bit number.  On modern computers, one assumes that could be handled in minutes.  ( https://stackoverflow.com/questions/4244319/how-to-find-all-the-prime-factors-in-a-unsigned-long-long-integer )