(Answer completely rewritten based on new information)
Does the TSA plan to implement rules that require every prospective student to seek pre-approval from a government agent (not just a flight school) prior to beginning flight training?
Not exactly. US citizens can still start flight training whenever they want. But from April 1, 2016 pre-approval from "a government agent" (the TSA) is required prior to soloing. Foreigners will still need TSA approval before starting flight training.
The final rule on this has now been published in the Federal Register and the TSA will indeed vet all student pilots, as of 1 April 2016 (my emphasis):
This action requires applicants to apply for a student pilot
certificate through a Flight Standards District Office, designated
pilot examiner, airman certification representative associated with
a pilot school, or certified flight instructor. Aviation Medical
Examiners will no longer issue a combination medical certificate and
student pilot certificate. Student pilot certificates will be issued
on the same medium as other pilot certificates and will have no
expiration date. All student pilot certificates issued before the
effective date of this final rule will expire according to their
terms unless they are replaced by another pilot certificate. This
final rule responds to section 4012 of the Intelligence Reform and
Terrorism Prevention Act and facilitates security vetting by the
Transportation Security Administration of student pilot applicants
prior to certificate issuance. This action withdraws the proposal
for pilot certificates to include a photograph of the individual
pilot.
But note that a student pilot's license is still not required in order to start training, it's only required in order to solo. So under this new rule, a US citizen can start flight training as usual, but can't solo until he gets TSA approval for his student pilot application:
IRTPA [the Intelligence Reform and
Terrorism Prevention Act] required that security vetting of all individuals, including
pilots, must be successfully completed by TSA before the FAA issues
a certificate. Therefore, applicants for student pilot certificates
must be vetted to receive their certificates and operate an aircraft
as pilot in command.
This also means that AMEs will no longer issue student certs, only medical certificates. The FAA expects that processing will take several weeks, which may be an issue for accelerated training programs that aim to get you a full pilot's license in a month or less:
The FAA estimates that the turnaround time for student pilot
certificates can be reduced to an average of 3 weeks or less,
provided that initial security vetting by TSA indicates that the
applicant is eligible for the certificate.
There was also some concern that it wouldn't be possible for pilots to solo on their 16th birthday any more because of the processing time, but the FAA specifically addressed that point, essentially by asking students to submit their application well in advance.
On the 'plus' side, the new regulation specifically says that pilots licenses will still not have a photograph (at least for now), which would have added more time and costs to the whole process. And the new student certificates will be plastic, not paper.