All this is to say that Congress probably needs to meet strict scrutiny in order to prohibit the free communication of software source code. However, Congress does have a clear authority to regulate (nominally interstate) commerce. Prohibitions on the sale of software or devices with certain functionality might be kosher, but as I understand it, prohibitions on the distribution of software source code would face a much higher legal bar.
The compelled inclusion of backdoors in code you publish is unlikely to be Constitutional. Even if it did somehow become effective law, that would simply drive FLOSS developers underground. And like you say, code can be audited, projects can be forked, and the existing body of FLOSS software won't disappear overnight.
(IANAL)
If I'm understanding correctly, if the code is publicly available in source form, then it is a different situation then if it is sold as a product. As a result of this, you would be able to write whatever source code you wanted, and share it, but if you begin trying to sell it then you could be in legal danger.
If through some nightmare scenario it did become illegal to write software without a backdoor, then much of the existing FLOSS software that is affected would get forked and development would get moved underground.