Yes. It was about as bad as you seem to doubt it was.

Lets just look at the Navy since that is an easy example of how staggeringly deep the drawdown was post WW2.

On V-J day in August 1945 the Navy had in commission 28 fleet carriers(the Saratoga, Enterprise, and the Essex's, with more of them and the 3 Midway's under construction). Along with another 70 Light and Escort hulls, 2 dozen battleships of all vintage, and a total strength of near 7,000 ships of all descriptions.

Less than 4 years later in June 1950, as the North Korean military prepared to storm south the USN was not even 1/10th that size! Just 630 ships were then in commission, with literally thousands of others in mothballs, sold to other nations, or in the process of being sold off for scrapping or conversion to merchant/private vessels.

There had also been an attendant reduction in manpower, and in other formations, like the number of squadrons of aircraft on hand to serve aboard the carriers, or from shore. Now the carrier force did see less gutting compared to say, the amphibious train, but it was still bleak, 8 relatively new Essex hulls and the 3 Midways were retained as the backbone. Though had the war not broken out several more of these were scheduled to go out of service, while only some would be rebuilt and come back.

The Navy had also come out of the service unification debate as a loser to the Air Force. The cult of the strategic bomber seemed, when paired with nukes, to render most of the force projection capabilities of the Navy-Marine Corps team obsolete, and the Army superfluous beyond securing the air bases to launch said bombers. This of course is based on the presumption that one is prepared to use Nukes in a variety of circumstances, and not engage on a spectrum of conflict intensity with conventional forces. And while the Navy and Marines did manage to avoid losing many of their aviation assets, the fights were bitter, and contentious in an era of tight budgets, in one year, 1947, witch unification and the USAF advanced to a full peer service the Defense budget went from 45 billion to about 15 billion!

They had also seen the ship embodying their nuclear future cancelled under Truman. The USS United States would have been a large, flush deck, proto super carrier, which could carry nuclear armed heavy bombers. Meaning the Navy could provide a mobile, fast response nuclear arsenal. But the ship was cancelled as part of the continuing consolidation.

Truman had pursued a strict cuts policy through his first term, and continued it following his victory over Dewey in 1948, if anything it accelerated. James Forrestal, former Navy Secretary had been serving as the very first Secretary of Defense following the consolidation of the War and Navy Departments under one roof. But disagreements with Truman over budgets, the Soviets, and his apparent discussions about serving in a Dewey administration forced him out in Spring 1949. And in comes Louis Johnson a strict Truman loyalist, who orders the United States scrapped a week after her keel was laid and a month after he started the job. He also pushed for giving all the aircraft the Marine Corps had to the Air Force though that went nowhere.

This triggered what was known as 'the Revolt of the Admirals', the Navy Secretary resigned, and several senior leaders vented to Congress, and the press about the overly deep cuts. This was partly led by Op-23 a group in the CNO's office set up to defend Navy interests during unification, and run by then Captain Arleigh Burke. It also took aim at the Air Force's prized B-36 bomber, and its claimed deficiencies, and noted that SECDEF Johnson had served on the board of its manufacturer, Convair, prior to getting his new job. This resulted in several days of Congressional Hearings in the Fall of 1949, with the Service Chiefs of both branches, and JCS Chairman Omar Bradley, and the service secretaries all on the docket. In addition the Navy called out a who's who of senior leadership, King, Nimitz, Halsey, and Spruance all testified or submitted testimony. While the Air Force argued the plane, despite a troubled development, was successful, and that a large expensive Navy was not needed for national defense needs, nor was amphibious expeditionary warfare in the future. Due to public mudslinging and the Administration's being against the Navy they lost, and were shammed a bit for their tactics.

But 6 months later the Truman White House balks at using Nukes to defend South Korea, and is indeed told the naval forces on hand in 7th Fleet were paltry. Just a single forward deployed carrier in the Valley Forge and a gaggle of escorts, with the other closest a week away at Pearl in the Philippine Sea. And it would would be another 2 months till a 3rd carrier could join them(Boxer who was in California to spend some time in the yards), though for a brief period that fall, 5 carriers were operating off Korea. But that represented a huge redeployment, with the 3 Midways having to serve as the backbone of the carrier force in the Atlantic and Mediterranean, and other hulls brought on line.

The conventional forces of the other branches were about as withered, and with the writing on the wall Secretary Johnson was asked to resign in September 1950 as the bloody fighting escalated, and the time for extreme fiscal constraints was abandoned. Truman tapped General George Marshall for the job then who filled the role for a year after his tenure as Secretary of State.

So yes Truman was forced to confront the inability of the Navy to do what he was asking of it in the Summer of 1950, at least with any pretense to retaining a global presence to assure European Allies and put up appearances. But it was the result of a years long process and political battles in which he had won and gotten the end result he wanted.

I'd like to take a slightly different approach to answering your question by highlighting the role that the Republic of Korea (ROK) Army was intended to play in the US strategy for Korea. As background, since Korea was divided in 1945 there had been strong agitation for reunification both north and south of the border, and when this failed to materialise (first due to US-USSR disagreement, then due to the United Nations to make any impact on events in the north) both the north and south formed their separate governments. Both governments claimed sovereignty over the entire peninsula, and both made it very clear that they would use military action to defeat the other if necessary.

Now the American commitment to Korea was one which steadily suffered more and more from President Truman's determination to cut costs, covered by /u/DBHT14. In fact, under Truman's administration financial aid for defence under the Mutual Defense Assistance Program Korea was seen as a Category III nation, which only warranted 'token' assistance. The approved funds for Korea under this plan in its adopted form in October 1949 was only $10 million (out of a total of $1.3 billion across all the recipients).

Not only was the defence funding this low, but also the fear of South Korea invading the north in a bid for reunification led to the Americans refusing to provide crucial military equipment to the ROK. No tanks, few effective anti-tank guns, limited artillery and no offensive combat aircraft were sold under the 1949 MDAP - only small arms, ammunition and the like. In this regard, the US essentially left the ROK defenceless against the north, which had been supplied with enough T-34/85 tanks to equip a full armoured division by June 1950, as well as a small but potent air force of Yak-9s and Il-10s.

Furthermore, a Korean Military Advisory Group assessment of the ROK Army's combat readiness in June 1950 judged only 12 of the army's 66 infantry and reconnaissance battalions to be "completely trained and more than 50 percent combat effective". Given that the US expected the ROK to defend itself, this was not a good sign.

Add into this the US military's progressive withdrawal from South Korea following the creation of the ROK in 1948, which had been completed by mid-1949. As a result of this, not only were the ROK essentially on their own in the field (save for the advisory KMAG), but the nearest American units would then have to be hurriedly shipped in from Japan. Add into this those Americans' lack of preparedness - five years as an occupying force had softened the calibre of the forces under General MacArthur's command. Furthermore, according to Hastings:

It was a direct consequence of Johnson's policies, approved by Truman, that by June 1950 MacArthur's divisions in Korea* lacked 62 per cent of their infantry firepower and 14 per cent of their tanks; that 80 per cent of the army's sixty-day reserve was unusable, and the army in Japan possessed only forty-five days' supply of ammunition.

• I believe Hastings may have meant to say 'Japan' here - as I mentioned, the last US military unit was withdrawn from Korea in mid-1949.

Plus the first US force to fight in the Korean War - Task Force 'Smith' - mainly had to rely on the inferior 2.36-inch bazooka to combat tanks, and this was ineffective against the North Korean T-34s. This made their attempt at a blocking action near Osan fruitless, as the North Korean armour simply rattled past them.

So not only was the US military in a poor state by the outbreak of war in June 1950, but also it was going into the conflict to back up a poorly-trained, poorly-equipped ally of its own creation, and one which would quickly be put to flight by the appearance of North Korean armour all the way back to the Busan Perimeter. This made it impossible for the hastily-despatched US forces to form an effective line anywhere else.

I would highly recommend Allan Millett's The War for Korea, particularly volume I for detail on the road to 1950, from which much of my answer is derived. Max Hastings' The Korean War also has some useful information, and Gordon Rottman's Korean War Order of Battle is a very useful reference book for the subject.