Profs telling me to contact them later.. for LOR HELP!!

2ne1

7+ Year Member
Oct 27, 2009
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Pre-Dental
I posted a few threads about my desperate need to get LORs before.
So, I asked two science profs that I got very good grades with (A+) and they are known to be "popular" among students at my college (they are good lecturers and very nice to students).
And they both said to me.. that they are packed with so many requests right now that they cannot say yes/no to me. They told me to email them a few weeks later and see if their lists are cleared off. They told me that it's not a NO, but also said they cannot commit as of now.
Is this common among profs? If you were in a similar situation, did you end up getting a letter?
Also, by when should I have all the letters to be considered "early"?

I am pretty bummed as I only have 1 science letter and a possible generic one(not sure yet). I have already asked most of science prof I got good grades with..Should I just wait until they give me the answer?