In 1965, President Johnson gave a speech in which he said, "In recent months attacks on South Vietnam were stepped up. Thus it became necessary for us to increase our response and to make attacks by air. This is not a change of purpose. It is a change in what we believe that purpose requires."
How did this incrementalism affect the results of the war effort?
When President Johnson gave this speech, he was justifying the US “Rolling Thunder” bombing campaign. This was an escalation in the war and it was accompanied by the first American ground troops in Vietnam. They were ostensibly there to protect the Rolling Thunder airbases but they soon came to experience “mission creep” and they became more involved in actual ground combat. It is hard to say whether a more decisive and unlimited approach to this war would have been more effective. Clearly, the strategy of incrementalism did not work.
This incremental strategy clearly did not work because the US did not win the war. It did not work because the North never really showed any inclination whatsoever to negotiate an end to the war. What is not clear is whether some other approach would have worked better.
We can argue that the incremental approach allowed the communists to get used to the gradually-escalating amounts of pressure being placed on them by the US. We can argue that the US could have crushed them militarily and in morale terms if it had committed all of its might to the war all at once. This would have had more of an effect on the communists and it would have seemed more purposeful and decisive to people on the homefront.
However, this is mere speculation. We cannot know what, if anything, could have allowed the US to win this war. All we can clearly say is that incrementalism did not lead to victory.