These ideas limited the possibility of American success in the war because they forced the US forces to fight with one hand tied behind their backs, so to speak.
Because the US government believed in the ideas of containment and of limited war, it was much less willing to be aggressive. The government, for example, was not willing to overtly invade Laos or Cambodia to decisively cut off the Ho Chi Minh Trail. The US also made no effort to invade North Vietnam as it did not want a more general war that might have involved China. Because the US was not willing to be as aggressive as it would have been in an all-out war, the chances for US success in the Vietnam War were somewhat limited by the ideas of limited war and containment.