I'm running off Grove's numbers for gun type and implosion weapons produced from new and existing reactors from in the latter half of 1945:
Month | Weapons |
August | 4 |
September | 3 |
October | 3 |
November | 5 |
December | 7 |
January | 12 |
And growing thereafter. The rundown of production IOTL is attributable to several factors:
1. The technical side of things. This was as you noted a question of funding and priorities as much as anything. No efforts were made between Summer 1945 and May 1946 to develop a means of recovering uranium fuel, and once a theoretical solution was established in 1947 it wasn't fully tested until 1949. Even then, the REDOX process wasn't implemented at all in production until 1951 - by that point investments in replacement Hanford reactors alone had yielded a steady rate of 10 bombs/month from June 1948 to June 1950. A continuing Manhattan project would have the resources and manpower for substantially more reactors and make intense efforts to develop a quick solution to the fuel problem. A doubling or trebling of production as a result of a doubling or trebling of effort, funding, and resources seems entirely achievable.
2. The production process. Because of the disconnect between interagency wants and needs no efforts were made to expand the number of reactors or upgrade them between 1945 and 1947, with the replacement of the Hanford reactors with 2 new ones only starting in August 1947. The uranium facilities at Oak Ridge, which were producing 8x the fissile material as Hanford (Albeit, the uranium gun-type bomb used 3x the fissile material) went unused because no gun type weapons were being built - their inefficiency was unjustifiable given the limited resources available for devices in peacetime, but in wartime uranium devices were intended to be produced well into 1946. Once again, we're talking about political capital and resources imposed by peacetime, not absolute limits.
3. The political context. in 1945-47 the US was actively pursuing nuclear arms control and, potentially, the transfer of all nuclear weapons to a neutral UN-run agency to preserve global peace. This de-nuclearization agenda, combined with the massive budget cuts to the US military, made the nuclear stockpile or the military's use of it substantially less important than in August 1945. Between 1945-48 even the president had limited information about the size of the nuclear stockpile, US production capabilities, etc., nor did the US military and decisionmakers. The Atomic Energy Commission was rudderless in its first couple years of existence, with Truman only directing it to make nuclear weapons its primary purpose in 1948.
Based on these points, I think it's fair to conclude that the plans for mass production of nuclear weapons in 1945-1946 were entirely achievable with the organization and resources of the Manhattan Project. Looking at the state of US nuclear production in 1945-1950 and concluding that this was the best that would be achieved had the war continued is like looking at the demobilized US Army in 1948 and concluding that this was all the mobilized Army of 1945 could achieve in 3 years. The 10 bombs per/month achieved in peacetime with a limited number of reactors in 1948-1950 should be considered a floor, not a ceiling (Not that 10 bombs/month falling on Germany is a small number either).