It depends on how this scenario plays out. Are you saying we do not Americanize the war in 1964/1965? I think the loss of South Vietnam despite American efforts would be the more complicated scenario. By that point, Humphrey has distanced himself from the war anyway, so Johnson would be left alone with the bag, although there may be residual ire from the people who supported the war and saw it lost, and lives and effort wasted. But, on the topic of no American ground fighting in the war, it is going to depend on Americanization. Is LBJ making Vietnam an issue, and sending bombers and all the rest without boots on the ground? Because if it is just a status quo pre-1964 situation with American involvement in Vietnam, it probably is not going to matter. Before we sent in the Marines, Vietnam was one of many flashpoints on the map, which most Americans could not point to on the map, if they had even heard of it at all. William F. Buckley may lament, but to the farmer in Iowa it isn't going to mean diddlydick. It would be like hearing Nepal fell to rebel Communist forces. That is a fear in terms of the Cold War and international Communism, but the focus would be more on the Sino-Soviet threat and not on the nation itself, and it would be a drop in the bucket.
That is the thing. Our actual history puffed up Vietnam into such an issue that it is hard to think of it as something that could have not really mattered to Americans. And it easily could have, because it did not matter to Americans until we sent ground forces. It was a small third world country of limited economic prospect and no ability to project influence on a global scale. It could easily have fallen into the ether of history, just like Laos, another place where we could have had a quagmire war which we avoided and now who remembers Laos or argues that it would have crippled the sitting president to not go into a war in Laos (which we ended up not doing)? There are parallel realities where this thread is "WI: Loss of Laos in the 1968 Election", or "WI: Loss of Algeria in the 1968 Election", where there are these are forgotten crises which were navigated without war, which became a big deal because of some parallel world's war and involvement and no one can see how they could be anything but pivotal and dominating.