Another excerpt on Vishnu Sahasranamam from the web

The Alwars to whom the Supreme Lord Narayana opened the flood-gates of Spiritual knowledge, shorn of discrepancies, deviations and ambiguities of sorts, were indeed above the Sages. They were full of compassion for the teeming millions of humanity, wallowing in the sty of samsara. It is significant that the Alwars have made frequent references to the Lords’s thousand names in their hymns. Nammalwar, the chief of the Alwar Saints, literally implored the people around to chant just any one of the thousand names of the Lord, though not all(Tiruvaymoli X-2-3). These names bespeak the Lord’s auspicious traits (Yani namani gaunani vikhyatani…), each of which is of unlimited dimensions. Actually, the Lord has innumerable auspicious traits, and, therefore His names, spelling out these traits should be innumerable. Who indeed can exhaust His infinite glory by compressing it within a mere thousand names? ‘Devo nama Sahasravan’ should not, therefore be taken literally to mean a mere thousand - the ‘Sahasram’ stands for ‘anantam’ - the endless(infinite).

‘Vaidya Sastra’ freely invokes Sahasranama japa for curing dire diseases , generally known to be incurable, ‘Mantra Sastra’ suggests Sahasranama japa for achieving the odds and ends of worldly life, ‘Karma Vibhagam’ prescribes the Sahasranama japa for all the ailments plaguing mankind and of-course Sri Visnusahasranama is a medicine for the disease of birth, death and re-birth, which is far more dreadful than the worst of bodily ailments.
At the end of the hymn, the potency of the recitation is brought by Sri Krsna Himself who said “Arjuna!, one may be desirous of praising by reciting the thousand names. But, on my part, I feel praised by one sloka. There is no doubt about it.” In this context, refer to name 685 in the hymn ‘stavapriyah’- He, who relishes being praised. He is pleased with anything that is uttered in His praise irrespective of who ever lauds Him, how he or she does it, and what language is employed.“ Engane collilum imbam payakkume (Tiruvaymoli VII-9-11).

Ayurveda mentions the recitation of sahasarnama as aiding the cure of many diseases with such sayings as “Diabetes gets cured by recitation pf Purusa sukta as well as the thousand names of Bhagavan;” “Similarly, Bhagavan’s thousand names must be uttered (for cure of tuberculosis);” “(For relief from fever), one must recite the Vishnu Sahasranama after conducting the Homa as aforesaid.” Even later poets such as Bana Bhatta, while describing a maternity ward has mentioned “The incessant chanting of Narayana’s thousand names too.” Sri Visnu Sahasranama is accepted with reverence as a panacea even by children, the dumb, dull-witted, women and atheists for recitation, meditation, exposition and comments to get rid of poisions, ghosts, disease, hauntings, sorrow, ill-omens etc., for getting absolved of heinous sins and worldly and other-worldly attainments.