The Soviet Union started the Space Race with Sputnik. The idea of a man made object whizzing overhead interested America. The fact that it was Soviet terrorized it. In the years after, the United States hoped to get a man into space ahead of the Soviets. Long term plans would be space, space stations, and landing on the moon by the mid-1970s. Once again, the Soviets beat Americans to space. Initially, America could only respond with a suborbital flight. While the US could tout this as achievements, the general mood was that the Russians were ahead of NASA, and were embarrassing the United States because of that lead. The Soviets also made the first spacewalk before the Americans could.
All these Soviet leads emboldened the United States to start and pursue it's Lunar program on a crash course. No longer would it be a long term side goal for some point in the decades ahead. It would be the goal, and dominate American space policy in the 1960s. However, what if it were the United States that made those early leads. Not necessarily a satellite before the Soviets, but what if the United States had the first man in space and took the lead from there? Would the United States have still been enticed to pursue a strong space program because of the newness and interest of space, and the competition with the Soviets? Or would we have been more apathetic? What would our space program look like if we put the first man up there, after the Russians had already had Sputnik? And how would the Russians have responded?
A little afraid to comment as when I do on this subject the thread tends to die... And on that note I'm guessing "name recognition" goes a long way on this site

Ignore a shield-wolf but once an Emperor mentions it every one listens
Pretty much everyone's "end goal" was getting to the Moon, but with a closer race I don't see it as having as much pressure as OTL and a lot less likely that someone could have gotten away with suggesting such a leap as came about.
(Michel; it was Ham's near fatal flight that delayed Shepard's. Butterfly that away and he would have been "first in space" which would have played a LOT better compared to Gargarin's orbital flight. Sure Yuri is still the first man in "orbit" but even a suborbital flight is closer than having nothing on the table at that point)
As I've pointed out elsewhere to keep even the USSR would have had to actually come up with a viable "plan" for competition or give it up. In OTL they simply tried to use what they had and keep putting up spectacles rather than a cohesive program like the American's and having America closer from the start would be much more incentive to do so I'd think. As it was they could bury their heads and cover their ears because the "lead" was so obvious to everyone from the start.
Eisenhower's general "response" that there was nothing to worry about and no cause for panic when everyone had ALREADY paniced and expressed very obvious worry was exactly the wrong thing to do on almost every level that it looks like he's completely out of touch with reality.
SPKACA: It wasn't inter-service rivalry but Ike's interference directly that prevented von Braun from being first. And given the circumstances and background with the development of spy-sats and over-flights it's really hard to fault the actual logic beyond Ike's dislike of VB's "Nazi" background. There's a good argument that America NEEDED to have the Soviet's put up a satellite first. Both to shake them from their complacency AND to have the Soviet's themselves "prove" the over-flight rights of satellites. Arguably though the US needed to have a more coherent program in place like having von Braun's team as an OFFICIAL "back-up" to the Navy, instead of betting everything on a single throw. The politics in the background is important too. At the time both the Army and the Navy were facing an environment where for all intents and purposes Ike had declared the Air Force the premier and sole provider of American security (New Look) and was simply tossing them scraps to keep them busy while he shut them down. Everything I've seen points that the Navy was given a go-ahead pretty much by default as the Air Force couldn't be "bothered" (the Atlas was finally given priority for development and the AF STILL was dragging its feet about development in the late 1950s but in any case wasn't going to be ready on the time table given) meanwhile the Army only had von Braun and Ike was very direct that he was NOT to be considered, which left only the Navy proposal. Being's it came from an office that could reasonably considered not "strictly" military Ike gets what he wants even if we don't manage to be first.
The problem was the Vanguard was no where NEAR ready or capable of what it was being asked to do and with von Braun's team specifically side-lined, well we got what we got.
nixonhead: Maybe on the military space flight program as the supposed actual purpose of NASA was two-fold. The first being to develop a "civilian" space program but technically the Navy Vanguard program was that because it could be argued that the NRL wasn't actually a directly "Military" program and second was to organize and consolidate the various "space programs" (the US had technically four or five at the time if you counted the Vanguard as separate from Navy development and the non-hardware stuff that NACA was doing) to be more efficient and avoid duplication. I'm pretty sure Johnson and other's in Congress were aiming in that direction and I"m pretty sure even if Nixon was in charge the consolidation would make a lot of sense. I think however that ARPA would have been a bigger component of such a program under anyone but Ike and what would be "NASA" would be more an agency rather than an administration under the circumstances.
To harp on my favorite butterfly/POD if the US had a bigger, more capable Atlas coming along I suspect a LOT of things would have been different. One thing though is without a direct and clear commitment to something like the Lunar Landing program I don't think the Saturn-V would have been developed.
Randy