This would be a complete repudiation of the Molotov-Ribbentrop Pact that the Soviet Union signed literally one month earlier and furthermore would be hugely detrimental to Soviet geopolitical interests. The United States would have really nothing to stand on: the US public mood was still heavily isolationist in 1939 and any US threat would be hamstrung by this. Isolationist sentiment in the US was well-known to European leaders of the era.
In addition to the aforementioned matters regarding Poland, the pact very clearly assigned much of Eastern Europe and even the Baltic States to the Soviet sphere. If Stalin destroys the Pact, the Soviets have none of these guarantees and the Germans can easily offer alliances to Soviet border states, which they would do without hesitation if the Soviets so openly violated a pact before the ink was dry. The Soviets would be in a nightmare scenario for this: immediate German hostility and the likely formation of a hostile alliance on their border to include countries that were forfeited to Soviet dominance historically.
But to get to the crux of why this wouldn't happen, it simply wasn't in Stalin's character to do. Stalin's foreign policy was one that could be characterised as having an excess of caution as opposed to Hitler who repeatedly made bold grabs for power and influence. Stalin's government had very, very steadily built up diplomatic and economic relations with the Western countries: finally achieving diplomatic recognition from the United States, France, and Great Britain and forming strong economic ties to buy Western industrial equipment and tools during the Great Depression. The Soviet Union also joined the League of Nations, being one of the last major countries of Europe to do so. This was coming from almost a decade of near-complete isolation from the international community with almost no diplomatic ties to much of Europe. Stalin's expansion and aggressive actions were things he always did with the utmost caution. Even on the eve of Operation Barbarossa in 1941, Stalin ignored a substantial body of evidence, including outright knowledge of a forthcoming German invasion from the Sorge Ring (a Soviet infiltrator in Japan who became aware of the invasion as a result of German efforts to entice Japan to join the invasion) because he was utterly convinced that German war preparations were a ruse to force him to strike first.
So really, a lot of issues about "why did Stalin not do X" come down to Stalin's personality and policies being extremely different from those of Axis leaders in this era.