I would go as far as to say that no amount of signatures would be enough to have any influence on a passing of a bill in congress
we have witnessed lots of examples when public opinion on a certain matter was discarded , lets recall the 2 million anti-war London protest or
the anti gay marriage protests in Paris : https://www.spiegel.de/international/europe/anti-gay-marriage-activists-clash-with-paris-police-a-890752.html
did it change the goverment's stance on the matters? the answer is no
so I would expect the signatures go as unnoticed as they can be