I think you can find a fairly reliable (more reliable than the Ethnologue, I would say) and pretty much consensual (meaning that even long-rangers would not object to it other than go much further in their speculations, hypothesizing deeper links between them) information in the Glottolog catalogue, as its authors generally tend to avoid controversial classifications that have not gained wider acceptance yet. It does not mean that at least some of the families and isolates are not related, but their relationship may be too deep to ever discover, or the research carried out so far has not met methodological standards, or, perhaps, no particular research into their relationship has been carried out yet.
Anyway, if you restrict the listing found on that Glottolog page to the North America and South America macroareas, you will get a list of top-level families and isolates including those that are not indigenous to the New World. Leaving the relative newcomers, pidgins, mixed languages, sign languages, unattested languages, unclassifiable languages and artificial languages out, you will get a list similar to the following:
NORTH AMERICA / Top-level families:
- Algic, Athabaskan-Eyak-Tlingit, Caddoan, Chimakuan, Chinookan, Chumashan, Cochimi-Yuman, Coosan, Eskimo-Aleut, Haida, Huavean, Iroquoian, Jicaquean, Kalapuyan, Keresan, Kiowa-Tanoan, Lencan, Maiduan, Mayan, Misumalpan, Miwok-Costanoan, Mixe-Zoque, Muskogean, Otomanguean, Palaihnihan, Pomoan, Sahaptian, Salishan, Shastan, Siouan, Tarascan, Tequistlatecan, Totonacan, Tsimshian, Uto-Aztecan, Wakashan, Wintuan, Xincan, Yokutsan, Yuki-Wappo
NORTH AMERICA / Isolates:
- Adai, Alsea, Atakapa, Beothuk, Cayuse, Coahuilteco, Comecrudo, Cotoname, Cuitlatec, Esselen, Guaicurian, Chimariko, Chitimacha, Karankawa, Karok, Klamath-Modoc, Kutenai, Maratino, Molale, Natchez, Salinan, Seri, Siuslaw, Takelma, Timucua, Tonkawa, Tunica, Washo, Yana, Yuchi, Zuni
BOTH NORTH & SOUTH / Top-level families:
SOUTH AMERICA / Top-level families:
- Araucanian, Arawan, Aymara, Barbacoan, Boran, Bororoan, Cahuapanan, Cariban, Chapacuran, Charruan, Chocoan, Chonan, Guahibo, Guaicuruan, Harakmbut, Hibito-Cholon, Huarpean, Huitotoan, Jivaroan, Kakua-Nukak, Kamakanan, Kariri, Katukinan, Kawesqar, Lengua-Mascoy, Matacoan, Nadahup, Nambiquaran, Nuclear-Macro-Je, Panoan, Peba-Yagua, Pri, Quechuan, Saliban, Tacanan, Ticuna-Yuri, Tucanoan, Tupian, Uru-Chipaya, Yanomam, Zamucoan, Zaparoan
SOUTH AMERICA / Isolates:
- Aewa, Aikanã, Andaqui, Andoque, Arutani, Atacame, Betoi, Camsá, Candoshi-Shapra, Canichana, Cayubaba, Chiquitano, Chono, Cofán, Culli, Fulniô, Guachi, Guamo, Guató, Irántxe, Itonama, Jirajaran, Kanoê, Kunza, Kwaza, Leco, Lule, Máku, Matanawi, Mato Grosso Arára, Mochica, Mosetén-Chimané, Movima, Muniche, Mure, Omurano, Oti, Otomaco, Páez, Pankararú, Payagua, Pirahã, Puelche, Puinave, Pumé, Puquina, Ramanos, Sapé, Sechuran, Tallán, Taruma, Taushiro, Timote-Cuica, Tinigua, Trumai, Tuxá, Urarian, Vilela, Waorani, Warao, Xukurú, Yámana, Yuracaré, Yurumangui, Yuwana
One of the great features of Glottolog is that it also collects all the relevant bibliographical references, so any research you would like to carry out yourself may well start right there. Check out the Haida listing, for example, where you can see the internal classification, useful comments and, of course, a long list of useful references.