I think @ObsessedNuker is mainly in the right: With lucky breaks, or a NATO spoiler attack in the air (the sort of thing that not only creates at least daytime air superiority, but might knock out most of the Elbe bridges), maybe they can hold them off for a few weeks. But probably on all odds less than that. Maybe 10-14 days.
NATO's precision guided munitions and technological edge in the air simply won't be enough to fully offset superior Soviet numbers and doctrine. The Soviets also have better tanks, better artillery - and NATO doesn't have the profusion of quality anti-tank weapons it would start getting with the Dragon in 1975, let alone the other big ticket weapons systems that were deployed later. The Soviets will pay a higher price in blood and fuel and munitions expenditures than they planned, but they'll get to the Rhine.
I think the 70's are one of the worst times of the entire Cold War for the West to fight the Soviets in Central Europe. More to the point: I think there's a fairly broad consensus on that today, with the quibbles being over the details of how NATO would lose, and the casualties for both. It's striking to me, in fact, that the skepticism of NATO's chances was shared at the time, even deep into the 80s - read
Carl Builder's 1989 RAND study, for example - it reads somewhat excessively pessimistic now (though many of its criticisms of US military culture were valid), but it's noteworthy what the expectations were back then.