The Japanese were indeed at the end of their rope by the tail end of the Russo-Japanese War, especially on land. The Imperial Japanese Navy had undoubtedly won a decisive victory over the Russian fleet, in a day reducing Russia from a first rank to a second rank naval power. The IJN had unquestioned mastery of the seas in and around Northeast Asia, but ultimately the aims of the war were to be found on the continent, where the Japanese had been engaged in a two front war. One front was the Siege of Port Arthur, which has often been held up as a premonition of the Western Front in World War I. The other, perhaps more interesting front, was the wider Manchurian front, where Japanese and Russian forces faced each other across the broad relatively open Manchurian plains.

On the land, while the Japanese were again victorious, the army's victories were far less one sided than the Navy's triumph as Tsushima. While the Japanese had been able to force the surrender of Port Arthur by seizing the hills overlooking the port and gaining the ability to direct artillery fire onto the ships in harbor, the victory had come at an immense cost in lives and materiel and was characterised by many amateurish decisions by senior Japanese leadership. To quote from Edward Drea's history of the Imperial Japanese Army:

[Lieutenant General Nogi Marasuke], for instance, a veteran of the restoration wars, the Satsuma Rebellion, and the Sino-Japanese War, was stumped when looking at a topographic map of the Port Arthur defenses. Unable to understand terrain contours or elevations, concluded the shortest distance between two points was a straight line and ordered an attack into the most difficult and best-defended terrain, where his troops suffered enormous and unnecessary losses.

On the Manchurian front, the Japanese were unable to deliver the sort of early knockout blow of Russian land forces that they hoped. Japanese planning had hoped for a double envelopment of Russian forces around Liaoyang, but while the Japanese had taken the city, they had failed to surround the Russian forces there and had taken such severe losses that they were unable to pursue. While the Japanese successfully defeated Russian counterattacks the fighting in Manchuria ground to a halt until the fall of Port Arthur in January 1905 freed up General Nogi's 3rd Army to move north. The subsequent battle for Mukden was a similar story to the earlier engagement at Liaoyang. The Japanese sough to force a double envelopment that would enable to encircle and destroy Russian field armies in the East, and while they managed to encircle a portion of the Russian force and take the city of Mukden proper, Japanese forces had sustained incredibly high casualties and lacked the strength to pursue the weakened Russian forces. Harbin, only 250 miles north was out of reach. While the Japanese had control of southern Manchuria, they could not continue the campaign into the north, let alone threaten Khabarovsk or Vladivostok, or campaign into Siberia.

By the time of the Battle of Mukden, the Japanese logistical situation was incredibly dire. Nearly the entirety of the Imperial Japanese Army was deployed in and around Mukden for the battle there. There was no strategic reserve, Hokkaido had been stripped of defenses, and Japanese forces in the Home Islands amounted to a handful of freshly raised divisions. Despite Mukden being the anticipated battle where Japanese forces were to isolate and destroy the Russian army, Marshal Ōyama, the overall commander of Japanese forces in Manchuria, had to issue instructions that his artillery forces be frugal with their fire, because there were no reserve artillery shells to restock from. Similar logistics issues prevailed throughout much of the Japanese army in Manchuria, including limitations in available replacements--both for soldiers and officers--and limitations in food supplies meant malnutrition spread amongst Japanese forces. Despite the capture of Mukden and the defeat of the Russian Army, these logistical issues ensured that the army was exhausted and that the war would have to come to a diplomatic settlement.

It's impossible to speculate on how the war would have continued if it had dragged on. Undoubtedly has the impact of military defeats not made St. Petersburg more concerned with domestic unrest than war in the Far East, perhaps the Russians could have massed enough of a force in the East to overwhelm the Japanese. As has been discussed, the Japanese were definitely on their last legs as well. Perhaps the Japanese could have continued to hold Mukden and their conquests, but we can't really speculate on that. Regardless, while the naval side of the Russo-Japanese War certainly ended in a decisive Japanese victory, the land phase was far more questionable, and while the Japanese had emerged victorious, the Imperial Japanese Army had been practically bled white and was on the tail end of its logistical tether.