Expect his approval rating to remain more or less where it is and always has been. His approval rating is hard baked into the system
Also the analysts who are linking this as a victory for Putin are probably looking in the wrong direction. This decision clears the way for Turkey to occupy the border area and clear the YPG back. The Kurds (who Trump once said had been very badly treated and let down etc) will be the victims.
So why is Trump crawling to Turkey you might ask? Well because the Saudi's pull his strings, and the Turks also have the Saudi's in a tight spot right now. This is a deal. Stop embarrassing the Saudi's and I'll let you do what ever the hell you like to the Kurds
Also this decision blindsided everyone, and 48 hours after Michael Flynn's sentencing was deferred with a US judge telling him that he'd "sold his country out" and that he could legitimately be considered as treason. Flynn you'll remember transpired to be acting as an undeclared foreign agent (Trump put him in charge of National Security!). But who was acting on behalf of? Turkey. Flynn's sentencing has been deferred whilst he is allowed to reflect on whether there is anything else he feels he ought to perhaps be sharing with the authorities. Is there any business links involving Turkey, or could Turkey themselves leak some damaging information which puts Trump in the crosshairs? Who knows
My instinct however is that this isn't a Putin thing, but instead it routes through Turkey and is all about Trump trying to protect Mohammed Bin Salman. Ironic to see the American President crawling and apologising for the cradle of Wahhabism isn't it. Go on Donald say it again so we can all laugh "radical Islamic terror"