The poles then gather a force of some 60k men and laugh a counterattack that proves to ve successful as they take Chernigrov with the aid of their Tatar allies crimea.
I'm not sure if the PLC ever fielded army as big as 60 000 soldiers. Such an army is expensive and gives its commander a lot of political power. Not to mention PLC still had a problem with the Cossacks.
However, there was a real chance of Polish-Cossack-Crimean alliance against Russia in 1650, when tsar Alexis tried to use PLC internal troubles (known as Khmelnytsky's Unprising) to his advantage. Crimean Tatars offered Poles support against the Russian and Khmelnytsky himself was not against such an operation, as long as Polish army stayed away from Ukraine. Unfortunately the Sejm prefered to send Polish troops against Cossacks.
Had the Sejm decided to join forces with Cossacks (who wopuld probably demanded to become the third part of PLC, similar to Poland and Lithuania) and Crimean Tatars, Russia would have lost such a war. Janusz Radziwiłl was a talented commander and with much bigger army (say, 60 000?) at his disposal could have defeated the Russians. What next?
First of all, Russia is knocked down for some time (not for very long, but long enough). Second, Ukraine becomes a third part of the Polish-Lithuanian and now also Ruthenian Commonwealth. Third, PLRC holds Smolensk and gains some lands, probably in Livonia and Russia.
The most important thing is: no Deluge. Charles X Gustav would have not dared to invade the Commonwealth if Warsaw had big, hardened in battle and victorious army. He did IOTL because Polish defeats against Russia and Cossacks and internal turmoil left PLC almost defenceless.
Ufortunately this scenario requires a big dosage of common sence injected right into the King and the Sejm's collective butt.