As previously stated, there is no threshold amount.
If entering the corrected form in place of the old one results in tax due, you will need to amend the return, however you need to wait until the original has been processed. There is a chance the IRS will correct the return in which case they will send a letter notifying you of the change and asking if you agree.
If the change results in tax, make sure that additional tax is paid by April 15th.
HERE is a link about making a payment without a return in case you need to pay before amending.
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