The government just needs to convince lawmakers they've come up with a scheme where only they can access the backdoor, not criminals. The opponents scream, "that's impossible," but LEOs only need to persuade lawmakers it's unlikely the backdoor will be compromised and they've won the argument with "good enough." If there's a terrorist attack and they claim weak encryption could've prevented it, "good enough" will suffice.
The more important argument is the government has repeatedly demonstrated they can't be trusted with the special access and they're pretty much guaranteed to abuse it. They'll even exploit those backdoors to spy on the very politicians from whom they're trying to get the new authority.
The threat of the government using new powers to violate the 4th amendment rights of innocent citizens is orders of magnitude higher than the threat of sophisticated criminals exploiting LEO backdoors.