This fact seems to suggest that if humans were able to migrate across thousands of miles of ocean from--I dunno, China I guess--to Hawaii, then sailing from Hawaii to North America should be manageable.
The first people in Hawaii came from the Marquesas and Tahiti, to the south, which is still quite a long distance. If you trace back the Polynesian expansion (and the expansion of their pre-Polynesia ancestors) from there, you eventually work your way back to Taiwan, all in the last 8-5,000 years.
Yet I don't believe we have any DNA evidence of Pacific Islanders within modern Native Americans, suggesting that the Native Americans did migrate from Asia but only by land and not by sea. But with the technology, equipment, and supplies available to them, could the Polynesians theoretically have been able to travel from Hawaii to California or Mexico?
The Americans were settled from northeast Asia, though it is increasingly looking like they did use boats to travel along the coast initially to largely bypass Canada and get into what's now the US prior to 16,000 years ago. But otherwise, yes, the Americas were not settled via by Polynesianesque trans-Pacific voyaging.
That said, that doesn't mean that there aren't Polynesian genes in the Americas. Back in 2013, "Polynesian" genes were found among the Aimoré (called the Botocudo in the article). There's some debate on the when and how these genes would have gotten into the Aimoré population, hinging on the unsettled question of whether it was the result of pre-Columbian or post-Columbian contact. If post-Columbian, it's more likely that this is these are actually Austronesian genes (Polynesians being a subset of the larger Austronesian population) that arrived in Brazil via slaves taken from Madagascar.
Looking at the equation the other way around, there's much more reliable evidence for [American genes in Polynesia](http://www.cell.com/current-biology/abstract/S0960-9822(14)01220-2?_returnURL=http%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS0960982214012202%3Fshowall%3Dtrue) as the result of Pre-Columbian contact. The study found that about 8% of the genome of the native Rapanui of Easter Island (the Polynesian island closest to South America) was of American origins about 20 generations ago - sometime in the 1300s or 1400s.
As /u/AgentEv2 said, there's also the evidence from the spread of sweet potatoes through Polynesia from South America. /u/b1uepenguin does an excellent job explaining that in the linked post, though I did just notice that he says kumar is originally a "Central American" word, which is incorrect. It's originally Andean, specifically Quechua, the language of the Inca empire. I've seen some attempts to link it to a specific dialect (mainly those spoken in Ecuador, which coincidentally was the epicenter for Pre-Columbian maritime trade in the region. People in coastal Ecuador had been sailing to Central America and possibly southern Mexico for hundreds of years prior to any potential Polynesian contact. Tupaq Inka Yupanki, the grandfather of Athualpa (the emperor at the time of the Spanish Conquest), conquered this area and, according to early colonial histories, heard of traders arriving from the west. He used the Ecuadorian boats to explore the Pacific for nine months and returned with foreign captives and bones of exotic animals (the colonial era informants said it was the jawbone of a horse, but if Tupaq Inka Yupanki really undertook this voyage and brought back such evidence, it was more likely a pig unless he managed to sail across the entirety of the Pacific and back in only 9 months). There's also some highly contested evidence from potentially Pre-Columbian chicken bones in South America that would support the Polynesian contact theory, but studies keep going back and forth on whether the dating of these bones is actually Pre-Columbian and whether they're genetics aligns them closer to Polynesian chickens or European chickens.
As for the more specific Hawaii-California connection that you're asking about, Kathryn A. Klar and Terry L. Jones are very vocal proponents of such contact. Their main line of evidence is similarities between the sewn-plank construction of boats in Polynesia and among the Chumash and Tongva of the southern California coast and alleged linguistic connections related to such technologies. Personally, I'm not convinced by their arguments, which helps fuel the Polynesian contact argument. Unlike the Quechua -> Polynesian adoption of the word kumar for sweet potato, Klar and Jones' argument depends on the Chumash adopting words tangentially related to their Polynesian counterpart. For example, they suggest that the Chumash word for a sewn-plank canoe, tomolo, is derived from the proto-Hawaiian tumulaakua, meaning, basically, "tree trunk." Additionally, while tomolo use similar construction methods as Polynesian sewn-plank vessels, the final product is quite different. Additionally, while the base construction methods are similar, the specifics of the design are quite different (tomolo tend to be much smaller and their planks of generally uniform size and shape; in the Pacific the vessels are much larger, with planks of varying size and shape to form specific parts of the vessel). The Chumash and Tongva, prior to European contact, didn't use sails, which one would assume they would have picked up from Polynesians if they were learning from Polynesian shipwrights. There are a few other points in Klar and Jones' argument, but over all I find independent invention of similar techniques a more likely explanation than direct contact.