Not really. You can get an FHA loan with only 3% down.
The bigger factor sellers look at is how much money you offer them. At 20% on a conventional, you may be able to get your lender to wave the appraisal requirement, which would be a help if you try offering much over the list price (unless you also have the cash to make up the difference, which if you need the 3% down payment, you probably dont).
Let me give an example to explain why they see it and why it's important. let's say that the agreed contract says that the buyer and seller agree to pay $600,000 for the house. Let's pretend that you have 10% down or $60,000 down. You need a loan for $540,000
The loan requires an appraisal to make sure that the bank (the loan) is a safe investment. The bank/loan only agrees to lend you the amount the house appraises at.
Back to the example and the appraiser comes out and says that the house is worth $500,000. In this case, again the signed offer says $600,000 with a $60,000 deposit.
The buyer either has to bring $100,000 to the table or the seller has to agree to make less money than the original offer (or some combination of the two) , but the bank will only give $500,000.
So if a buyer had a $100,000 downpayment and offered $600,000 and a second buyer offered $600,000 as well but only had $60,000, the seller would most likely choose the offer with more money down. it would be more likely to close.
Hope that helps
And in warm markets (for get about hot markets like NY and SF), even an offer with 20% down is not pleasing to the seller. 20% or less down means that if the bank under appriases for whatever reason would cause a massive delay and/or cause the deal to fail.
For the buyer, many costs at this point or unrecoverable. Inspecting, lawyers, etc. This is a huge hit to a low income person.
In a warm/hot market, anyone with a mortgage is going to lose to someone with cash, so not really an issue.
Anecdotally from friends buying their first homes, very few to zero of them put down anywhere near 20%.