The major "loser" here is going to be Kennedy, history will NOT be kind. (And as he's no longer going to be the patron saint of space-nerdism due to his "killing" the American Space program over this whole 'coopertive' bunk his place in history will be even muddier 
)
In general two things will happen when the 'cooperative' program goes through: NASA is going to find itself suddenly very marginally funded really There quickly and the US Air Force will finally have a valid 'excuse' to fully separate its space program from that of NASA. (Much to both Kennedy's and McNamara's discomfort) The Titan II SLV, being basically a 'man-rated' Titan II ICBM will not be available for NASA use, (nor any of it's variants) and overall "military" support for NASA and its missions will drop significantly. NASA has just become a 'security' risk. This will also mean that DoD (aka NSA launches) will rapidly move from the Cape to Vandenberg and any and all launchers used for such, (Atlas-Centaur, and Thor-Delta for example) will no longer be available for NASA use or launched from the Cape.
Arguably this will give Von Braun's Jupiter more play time as well as variants of the Saturn-1 family but at the same time the Air Force will be justified (through the DoD/NSA) in demanding development of various Titan and Delta, (Thor-Delta) launch vehicles. Unfortunately, (I see Archibald and the rest of the "Big Gemini/MOL" crowd salivating in the wings there don't think I don't! ) while Blue Gemini may get some additional traction, (as an 'alternative' to the slow progress of the official 'Apollo' program) MOL is still unlikely as NASA will have justification to push for MORL based on the Saturn-1 LV and Apollo CM/SM. Speaking of you realize that the "Apollo-1" disaster is still likely? And the fallout will be worse given more 'methodical' push the Soviets will be inclined to pursue given a cooperative program. The lack of time pressure may be enough to allow the bugs to be ironed out before they become hazards though so it may be a wash.
Oddly enough, and frankly there's no real way to 'work-it-in' but an interesting point at this time, (about 1964 I think) McNamara was made aware that the Air Force REALLY wanted to invest in and develop the Orion propelled "Deep Space Deterrent Force" with memo's indicating they wanted it badly enough to devote a significant portion of their operational budget to the development. Though interesting there is no way the Soviets are going to green light the US putting such a system into development let alone operation and the needed infrastructure to build and deploy what amounts to hundreds of thousands "tactical" nuclear bombs per year isn't acceptable to Kennedy either. NERVA will also be taken away from NASA at this point as the AEC has to many ties to both the weapons design and develoipment branches of nuclear engineering to be acceptable.
Further Von Braun and companies more 'natural' conservatism is going to come to the fore as they insist on more and more rigorous testing of each phase of the program which was bypassed in the name of time in OTL. For example the 'testing' phase of the Saturn-V will be greatly extended as each stage is tested rather than the "all-up" test of OTL. Much like the Saturn 1 flight tests where the first stage with two dummy upper stages was flow a couple of times, then a marginally operational second stage and so on.
As for public reaction as you've noted it's not that much of an issue with them as we were by the mid-60s seeming to have 'caught up' at least with the Soviets in space. Further though Kennedy HAD been desperate to find any alternative to choosing to go to the Moon. Only doing so when it was clear that no other 'goal' could have the effect he wanted. By 1965 the majority of the build-up spending for NASA had been done and the budget was due to drop anyway. (See https://en.wikipedia.org/wiki/Budget_of_NASA, see specifically the 1964/65/66 time period) Once the 'goal' loses his support in favor of the cooperative effort it will rapidly drop off the public radar for "other" priorites more applicable to their needs.
As usual if you need more info
Randy
)In general two things will happen when the 'cooperative' program goes through: NASA is going to find itself suddenly very marginally funded really There quickly and the US Air Force will finally have a valid 'excuse' to fully separate its space program from that of NASA. (Much to both Kennedy's and McNamara's discomfort) The Titan II SLV, being basically a 'man-rated' Titan II ICBM will not be available for NASA use, (nor any of it's variants) and overall "military" support for NASA and its missions will drop significantly. NASA has just become a 'security' risk. This will also mean that DoD (aka NSA launches) will rapidly move from the Cape to Vandenberg and any and all launchers used for such, (Atlas-Centaur, and Thor-Delta for example) will no longer be available for NASA use or launched from the Cape.
Arguably this will give Von Braun's Jupiter more play time as well as variants of the Saturn-1 family but at the same time the Air Force will be justified (through the DoD/NSA) in demanding development of various Titan and Delta, (Thor-Delta) launch vehicles. Unfortunately, (I see Archibald and the rest of the "Big Gemini/MOL" crowd salivating in the wings there don't think I don't!
) while Blue Gemini may get some additional traction, (as an 'alternative' to the slow progress of the official 'Apollo' program) MOL is still unlikely as NASA will have justification to push for MORL based on the Saturn-1 LV and Apollo CM/SM. Speaking of you realize that the "Apollo-1" disaster is still likely? And the fallout will be worse given more 'methodical' push the Soviets will be inclined to pursue given a cooperative program. The lack of time pressure may be enough to allow the bugs to be ironed out before they become hazards though so it may be a wash.Oddly enough, and frankly there's no real way to 'work-it-in' but an interesting point at this time, (about 1964 I think) McNamara was made aware that the Air Force REALLY wanted to invest in and develop the Orion propelled "Deep Space Deterrent Force" with memo's indicating they wanted it badly enough to devote a significant portion of their operational budget to the development. Though interesting there is no way the Soviets are going to green light the US putting such a system into development let alone operation and the needed infrastructure to build and deploy what amounts to hundreds of thousands "tactical" nuclear bombs per year isn't acceptable to Kennedy either. NERVA will also be taken away from NASA at this point as the AEC has to many ties to both the weapons design and develoipment branches of nuclear engineering to be acceptable.
Further Von Braun and companies more 'natural' conservatism is going to come to the fore as they insist on more and more rigorous testing of each phase of the program which was bypassed in the name of time in OTL. For example the 'testing' phase of the Saturn-V will be greatly extended as each stage is tested rather than the "all-up" test of OTL. Much like the Saturn 1 flight tests where the first stage with two dummy upper stages was flow a couple of times, then a marginally operational second stage and so on.
As for public reaction as you've noted it's not that much of an issue with them as we were by the mid-60s seeming to have 'caught up' at least with the Soviets in space. Further though Kennedy HAD been desperate to find any alternative to choosing to go to the Moon. Only doing so when it was clear that no other 'goal' could have the effect he wanted. By 1965 the majority of the build-up spending for NASA had been done and the budget was due to drop anyway. (See https://en.wikipedia.org/wiki/Budget_of_NASA, see specifically the 1964/65/66 time period) Once the 'goal' loses his support in favor of the cooperative effort it will rapidly drop off the public radar for "other" priorites more applicable to their needs.
As usual if you need more info
Randy
