So, the kind of chaos in the USA, the unknown development in the USA scared the USSR which feared for America's possible response and this in turn finally made them to abandon any plans of the military invasion of the Warsaw Pact. Almost immediately after, general Jaruzelski was appointed the chief of the govt and the preparations for the Martial Law to stifle the Solidarity with internal forces began in full swing.
My understanding is that Jaruzelski begged the Soviets to invade and they told him “no”, and from there he decided to implement Martial Law using the threat of Soviet Invasion (which he knew wasn’t coming).
In the speech Reagan gives before assassination attempt he does make reference to Poland.