After the 2002 peso collapse, with upwards of 20 percent unemployment, remunerative work was hard to come by even for legal residents, let alone visitors on tourist or student visas. Even then, foreigners found work teaching English or another foreign language, working in the tourist industry, or performing casual labor in bars or restaurants. The problem with such jobs is that they either require time to build up a clientele (in the case of teaching), may be seasonal (tourism), and can be poorly paid (restaurants, except in a handful of places where tips are high). Language teachers, in any event, may find that few Argentines can afford the luxury of one-on-one lessons.
Ideally, obtaining a work permit from an Argentine consulate is better than attempting to obtain one in-country, as employment may not begin until the permit is actually granted. No matter what, the process requires submitting documents and takes some time.