There is a (seemingly) little-known halakhah in the Mishneh Torah which leaves absolutely nothing to the imagination of whether or not it is desirable or permitted to make living from learning Torah.
The Rambam writes the following in Hilkhoth Talmudh Torah 3:10:
Everyone who determines in his heart that he will be occupied with learning Torah and will not engage in labor, and therefore sustain himself from public charity - behold, such a one profanes the Divine Name, denigrates the Torah, extinguishes the lamp of the Jewish religion, brings evil upon himself, and removes his life from `olam haba because it is forbidden to benefit from the words of the Torah in this world. The Sages said, "Everyone who derives [monetary] benefit from the words of the Torah removes his life from the world [to come]." They further commanded and said, "Don't make them [the words of the Torah] into a crown to make yourself great with them, nor a spade with which to till the ground." They further commanded and said, "Love engaging in labor and hate the service of being a public rav. And all study of Torah that is not accompanied by engaging in labor, in the end it is worthless and the one who engages in such [exclusive Torah study] will in the end become one who steals from his fellow creatures."
Now, everyone needs financial help (i.e. hesedh and ssedaqah) at certain times throughout their life, and to varying degrees. However, the Rambam writes in the next halakhah (3:11) that:
It is a great virtue for one to be sustained through the work of his own hands, and to do so was a character trait of the ancient devoted ones (the "hasidhim rishonim", a group often mentioned in the Mishnah for their particular piety and devotion to God). And in doing so, one will merit all of the honor and goodness that is available in this world and in `olam haba. As it says, "When you eat from the labor of your hands, you will be contented and it will be good for you" (Tehillim 128:2) - "contented" in this world, "good for you" stored for olam haba which is entirely good.
See also Hilkhoth `Eduth 10:14 where making a living from playing dice - or any other form of non-labor - is called "avaq gezel" (a phrase meaning, "not technically theft, but it might as well be"). In addition, it invalidates someone as being a reliable witness in a beth din.
And see also Hilkhoth `Aniyyim 10:18 which says:
A person should always push himself and exist in painful difficulty rather than cast himself on the mercy of the community. Thus the Sages commanded and said, "Make tyour Shabbath like a weekday and do not demand your needs from your fellow creatures. Even if a poor person is a greatly honored hakham, he should sustain himself through a trade, even if it is a miserable one, and not demand his needs from his fellow creatures. It is better for a person to spread out the tanned skins of neveloth in the shuq rather than saying to the people, 'I am a hakham, I am a great person, I am a kohen, so support me." And in this matter the Sages commanded us to do thus. Even the greatest of the hakhamim were woodchoppers, carriers of building materials, water drawers for use in vegetable gardens, smelters of iron and producers of charcoal, and they did not ask for charity from the community, nor would they accept gifts from the community even while serving the community."
So, there is no doubt that, YES, there is a halakhic imperative for a person to make a living to support himself.