Disclaimer: I don't have sources for this as I'm mostly summarizing various history classes and my experience in the high-native populated Alaska.

First you have to remember a few things: within "Latin America", you have Argentina and Uruguay (very low indigenous populations), and Perú and, as you mentioned, central America, with high populations that still speak Quechua and mosquito respectively.

Then, within the US, you have New York and Georgia, where native heritage is nearly forgotten, and Arizona and Alaska, where native heritage is easily found (the former in the form of reservations, the latter with immensely powerful native-only corporations and Yup'ik-only schools in much of the western part of the state). The point here is that there isn't such a uniform statement you can make about all of them between the two continents.

Then of course there are the vastly different policies put in place: the Spanish ran their empire as a source of wealth, settled by men searching for treasure who employed or coerced natives into their service after defeating several large (million-strong) empires that rivaled Europe in all but disease immunity and gun powder technology. From the start, average Brits were coming to the "new" world in search of a better life in the form of readily available land. This situation was mirrored in Argentina, which was an equal to the United states until the 20th century (search "argentine tragedy" on the economist website for the full story here). Argentina, which, as I mentioned, lacks a vibrant indigenous culture today, also attracted millions of Spaniards, Germans, Irish, and more. Argentina pre-contact was sparsely populated as far as I'm aware (1452 or whatever that book about China was), but obviously the areas on the eastern seaboard were different; we are all familiar with the removal policies propogated by Andrew Jackson, but of course there was the policy of British and French to ally with the neighboring tribal groups, treating them as sovereigns, while the spanish supplanted existing governments with their own: counterintuitive given the present cultural situation.

Which brings me to a bigger point then government: geography. It's relatively safe to say that isolated areas are keeping their indigenous heritage. In Ecuador, the easily accessed coast and area around Quito are entirely Spanish-speaking; in the Amazon, several hundred thousand people hunt, fish, and gather in Quechua, as is true in much of the Amazon - for now, until mining and logging companies change that. In Alaska, the Aleut culture (first to make contact, and its people the victims of forcible removal to concentration camps in WWII) has long been "in danger" as far as the language goes, and the same for Lingít, the people who lived near the Russian capital of Sitka and engaged the Russians in battle), which we are struggling to revive. Yup'ik, on the other hand, is spoken by several thousand people who continue to live their traditional lives in their ancestral language - in isolated communities in the harsh and enormous Kuskokwim river valley (and the same for many Iññupiat on the north slope. It's simply harder for foreign languages to penetrated where they don't present a daily necessity.

Tl;dr it started with policies of the colonial powers, but much can be attributed to geography, with similar cases in regions of both continents.

The simple answer is that prior to European colonization it is unlikely that more than 10% of the native population lived in North America this population discrepancy can largely explain why there are more people of native descent in Latin America. In addition Latin American colonization began earlier than in North America because of this by the late 17th and 18th centuries the remaining native population in Latin America had started to rebound as immunity to European diseases were built up. By contrast much of the native population of the United States wasn't exposed to disease, deportation and war until the 19th century dramatically lowering their numbers at a time when Latin American were recovering.