Opposition? Yes. Overthrow Not really.

In the 1920s the USSR was a party but not personal dictatorship. Which is to say, the CPSU had a monopoly on politics in the USSR but Stalin did not have a monopoly on policy-making and power within the CPSU yet. After Lenin's incapacity there was no single leader of the USSR, but rather a period of "collective leadership".

Under the Leninist principle of "Democratic Centralism", there is -supposed- to be real debate and disagreements within the Central Committee and the Politburo (the highest decision making bodies in the party). Opposition to any single person is supposed to be no more illegitimate than say, disagreeing with a major party official in a western parliamentary party, so long as that disagreement is kept within the party itself and all final decisions are presented as unanimous.

So in the 1920s Stalin did face opposition and himself played in factional politics. First by allying with politburo members Zinoviev and Kamenev against Leon Trotsky. Then after Trotsky's power was destroyed he allied with Bukharin and Rykov (The right opposition) against Zinoviev, Kamenev, and Trotsky (the united opposition) over the question of whether to continue Lenin's New Economic Plan. By the mid-late 1920s, he had politically defeated the left opposition and by the 30s the right opposition had being neutered as well. Essentially every figure in the Lenin era of party leadership was arrested and executed during the late 30s.

But even before that, there was never an analogue to the Schwarze Kapelle, what became the Valkyrie plotters, in the USSR. The closest thing to it might have being the Ryutin affair of 1932 in which a small number of opposition figures led by the former secretary of Moscow party commitee Martemyan Ryutin did try to circulate a pamphlet calling for Stalin's removal and repudiation of collectivization. However, the number of people implicated was relatively small and the attempt was promptly informed to the secret police. Ryutin and 23 of his accomplices were expelled from the party for one year. However, they were never readmitted and later arrested and executed.