Does the Python Software Foundation License permit relicensing to the GNU GPLv3 (or v2)?
You cannot re-license the individual PSFL-licensed work, because you are not the copyright holder and the copyright holder has not permitted you to do so. Python will remain under the PSFL; the only way to change this is for the copyright holder to issue it under a different license.
Instead, however, if you are merely interested in combining a PSFL-licensed work with GPL-licensed code, then you are interested in the question of whether the PSFL is GPL compatible.
The Free Software Foundation says of Python licensing for various versions:
License of Python 2.0.1, 2.1.1, and newer versions
This is a free software license and is compatible with the GNU GPL. Please note, however, that intermediate versions of Python (1.6b1, through 2.0 and 2.1) are under a different license (see below).
License of Python 1.6a2 and earlier versions (#Python1.6a2)
This is a free software license and is compatible with the GNU GPL. Please note, however, that newer versions of Python are under other licenses (see above and below).
License of Python 1.6b1 through 2.0 and 2.1
This is a free software license but is incompatible with the GNU GPL. The primary incompatibility is that this Python license is governed by the laws of the State of Virginia, in the USA, and the GPL does not permit this.
As long as you're not using a version of Python between 1.6b1 and 2.0 or version 2.1, your copy of Python is compatible with the GPL.
GPL compatibility does not allow you to simply relicense the Python interpreter in isolation, but it does mean that you can combine the interpreter with other works that are licensed under the GPL and license the entire combined work under the GPL, as required by the GPL.
In other words, you can comply with both licenses' requirements simultaneously. In the particular case of the GPL, this is possible because the set of restrictions imposed by the Python license is a subset of those imposed by the GPL.
If you get some code under the Python license, and you add some code you license under GPL, the result has to be licensed under the more restrictive license, i.e., GPL.
In any case, doing so is damaging. Your combination will become a pariah in the larger Python community, as it can't be included without tainting all. This is a sure recipe to have it die on the wine. The community will probably see you as disruptive, and shun you. Everybody loses.