Liber was one of the Bund's representatives at the fateful Second Congress of the RSDRP in 1903, and the third most frequent speaker at the congress (after Vladimir Lenin and Leon Trotsky). He defended the Bund's demand to be recognised as an autonomous organisation within the RSDRP and as the sole legitimate representative of the Jewish proletariat in the Russian empire. This position was roundly rejected by both Lenin and I.O. Martov, soon to emerge as the leaders of the Bolshevik and Menshevik factions of the RSDRP. Martov had himself been a member of the Bund in the 1890s and one of Liber's former collaborators, but at the second congress, he supported Lenin in demanding the integration of the Jewish proletariat in an All-Russian Social-Democratic party. Martov proposed a more liberal criterion of party membership than Lenin, but by the time that issue led to the schism between Bolsheviks and Mensheviks, Liber and his fellow Bundist delegates had withdrawn in protest from the congress and from the RSDRP. It was the Bundists' exit that gave Lenin a slight majority at the congress (and hence enabled him to call his faction 'Bolshevik' - 'Majoritarian').