How does machine guns = defensive warfare make the "Schlieffen Plan" impossible?
The Germans were able to advance to the doorstep of Paris. They continuously tried to engage the Entente in a decisive battle (from the Frontier all the way to the Marne). They were unable to do so because the Entente refused to be engaged that way, and because the Entente had superior strategic/operational mobility (they were retreating onto their own logistics and infrastructure (railroads)). At the Marne (Paris), Germany was at or near it's logistical limits. Germany also transferred 200,000 troops to the Eastern front.
The Battle of the Marne itself was not "Germany face tanks into prepared defensive positions and is stopped cold by Entente machine guns and fortifications". The battle was a retreating Entente force, bolstered by re-inforcements, turning around and attacking into the pursuing Germans.
The "Schlieffen Plan" failed before the whole 'static warfare' thing started. In fact, it was the failure of the plan that induced the conditions for the race to the sea, and the whole western front shitshow.
The "Schlieffen Plan" failed because Germany outran it's logistics, because Germany panicked when Russia mobilized faster than anticipated and transferred over a sizeable body of men, because France was able to use it's position (retreating onto its infrastructure) effectively (and they weren't dumb enough to try to engage the Germans at every opportunity), and I'm sure for many other reasons as well. Machine guns may play a part, but I think it's overly reductive to claim that "machine guns - defensive warfare" made the plan impossible.