No, the DSA mission is the eventual overturn of a capitalism via democratic process. Plenty of Trotskyists and Marxists in the leadership of the DSA. Even Marx himself wrote in the Manifesto that a transitional period from capitalism to socialism is more realistic rather than a sudden, jarring switch to socialism.

The Communist Manifesto goes on to spell out ten measures that the proletariat should take on coming to power, to transform the economy and society. None of these measures abolishes capitalism straight away; each constitutes a partial intervention by the state in the economic mechanism of capitalism, and only in the totality, and over time, are they deemed to undermine capitalism completely. Thus, for instance, the measure ‘a vigorously graduated income tax’ assumes that under the dictatorship of the proletariat there would still be marked differences in incomes – that the capitalist would not be expropriated at a stroke. ‘During the revolution, the gigantic increase in the scope of taxation may serve as an attack on private ownership; yet even in such a case taxation must be a stepping stone to fresh revolutionary measures, otherwise there will be a return to the erstwhile bourgeois conditions.’ [4]