Trotsky was disliked by the leadership of the party, and by many party officials as well since it was up to the General Secretary Stalin to appoint most of these officials.
However, Trotsky was quite popular with the Red Army (unsurprisingly, since he was a better general than Stalin and as People's Commissar of the Military had influence on the nomination of officers). I think that any leftist revolution in the early Soviet Union would in fact be a coup d'état lead by Trotsky as Commissar.
For a contrary view, see Roy Medvedev, *Let History Judge: The Origins and Consequences of Stalinism*:
"... The idea of a military solution to the internal party conflict occurred to some members of the Trotskyist opposition. Zinoviev, Kamenev, and Stalin had some apprehensions in this regard, which explains the changes made on the Revolutionary Military Council as early as 1924 and the removal of Antonov-Ovseyenko as head of the Political Directorate of the Red Army and his replacement by Bubnov.
"It must be said quite emphatically, however, that at the time of the discussion in the party there was never any real threat of a military coup, if only because the Red Army was never just a 'docile' instrument in Trotsky's hands. Trotsky could rely fully on the soldiers of the Red Army when he gave the order to march on Warsaw, but he could not have raised the Red Army against the Central Committee and the Politburo...
"If Trotsky in 1924 thought as he wrote in 1925, it would have been one more of his illusions... [A] military ouster of the triumvirate and the party apparatus loyal to it would have been an extremely difficult and uncertain undertaking--an adventure with very little chance of success. If Trotsky refrained from such a step, one can assume that what held him back was not concern over Bonapartism but uncertainty of his control over the Red Army.
"The German edition of Serge's memoirs contains a foreword by the prominent German revolutionary Wollenberg, who went to live in the Soviet Union after the failure of the German revolution and in the thirties fled to the West from the persecution of the NKVD and the Gestapo. Wollenberg convincingly disputes the version of events presented by Serge:
"'What a colossal mistake in assessing the concrete situation that had arisen in the land of the Soviets within a few months after Lenin's death! I must add that at the time Lenin died I was still on military duty in Germany. As a specialist in civil war I held a prominent post in the German Communist Party. At that time I thought along more or less the same lines as Serge and as Trotsky apparently thought about all these matters for another decade or more.
"'But when I moved to Moscow, I saw my error. In Moscow I was forced to realize that the leading figures on the Red Army general staff, such as Tukhachevsky, with whom I became friends, admired Trotsky greatly as the organizer of the Red Army, as a man and a revolutionary, but at the same time they took a critical attitude toward his general political position.
"'...I had very close contact with the army in general, and, through it, with the Russian village. There could be no doubt that the top military command had full confidence in the party leadership.... And in the entire party there was an unquestionable majority in favor of the triumvirate, that is, the leading threesome formed after Lenin's death: Zinoviev, Kamenev, and Stalin. That was the order in which the importance of the three members was estimated at the time--with Stalin last.
"'If the Soviet constitution could have been changed for a plebiscite to be held, it is impossible to say which of Lenin's successors would have gathered the most votes. But it can be said for certain that, given the hostility of the peasants and the middle class (which was reappearing in the first half of the 1920s) in relation to Trotsky, who was considered an 'enemy of NEP,' the outcome would have been rather unfavorable for him.
"'It is necessary to state this with full clarity because to this day Trotskyists of all varieties, as well as Soviet experts in West Germany and other countries, continue to spread the tale in speech, in print, on radio and on television that after Lenin's death Trotsky supposedly missed a 'sure bet.' Apparently Victor Serge believed this too right up to his death.'"
http://books.google.com/books?id=91fB88t2_zwC&pg=PA133