I am not an expert on the Indian Removal Act of 1830, but I literally just finished a tangentially related book, Conspiracy of Interests: Iroquois Dispossession and the Rise of New York State by Laurence M. Hauptman. Although the Cherokee Trail of Tears (which, factoid, happened under the presidency of Martin Van Buren, not Jackson) is the most infamous because of its high death toll, there was intense pressure on all Native American societies east of the Mississippi River to abandon their lands and move west. My knowledge is focused on the Iroquois, but the same general forces that led to Cherokee removal were at play with Iroquois removal in New York State. I will have to rely on someone else to give details (and correct any errors I might make) about the Southern Native American nations that saw the worst of the Indian Removal Act.

In in the first half of the 19th century, there was a boom of transportation improvements on the American interior. New roads and canalways, and eventually railroads, were making the settlements inlands from the coast very desirable to white settlers and capitalist endeavors. Land occupied by Indians was highly coveted.

Racism played a key role in Indian Removal, but not in a Holocaust-esque goal to exterminate a people. The racism of Indian Removal was a paternalistic dismissal of natives' abilities to take care of themselves, combined with a self-righteous conviction that the American way of life was the only correct one.

Americans in the 1830s saw the massively depopulated and impoverished Native Americans living segregated on lands near Anglo-American communities as the remnants of a once-great but dying "race." They saw the native cultures fraying and destabilizing around them and attributed Indian decline to contact with whites. Alcoholism was a very common problem in Indian societies at this time, and the alcohol was nearly entirely purchased from or gifted by whites.

Native American societies were typically more communal than were Anglo-American settlers. In 1830, American society was modernizing. There were many simultaneous revolutions happening: the Industrial Revolution, the Market Revolution, a transportation revolution, and a religious revolution (the Second Great Awakening). In all this change, the Indians seemed to stay static. Many misguided but well meaning charitable organizations (particularly among the Quakers) tried to "uplift" various Indian societies by exposing them to Western sedentary farming (as opposed to semi-nomadic hunting and horticulture), Western capitalist economy (with its emphasis on privately held land), and Christianity (with its cultural support for the previous two items). One of the greatest outcomes of this was the crumbling of traditional societies and cultural practices which were incompatible with Western "rugged individualism". This is easily seem in the ways land speculators and development companies ate away at treaty-guaranteed lands of the Iroquois by coercing and bribing individuals to privately sell communal native land.

A self-serving idea among influential policy makers. They believed that:

• Since the tide of American settlement could not be stopped, and
• Since the "noble savage" Indians were a "race" that would inevitably disappear because of their inability to adapt to "modern ways",

The only humane thing to do would be to find a tract of land somewhere out west, in the undeveloped West, where the Indians could be transplanted to. Out there, they would be able to live out their lives in a sort of cultural hospice, where the Anglo-American culture wouldn't bother them and vise versa.

Once Americans saw the devastation the Indian Removal Act had on native populations, there was a popular backlash against it. The Trail of Tears became something of an albatross around Van Buren's subsequent political fortunes.

TL;DR -

No, Americans did not know they were sending the Cherokee to their deaths. They largely bought into the myth that Native Americans were incompatible with Anglo-American society, and transplanting them to a new home was in the best interest of all parties. American policy makers and the public at large were willfully ignorant of any possible consequences.

Sources:

• Conspiracy of Interests: Iroquois Dispossession and the Rise of New York State by Laurence M. Hauptman

• The Death and Rebirth of the Seneca by Anthony Wallace

• A Shopkeeper's Millennium by Paul E. Johnson

As a followup: If they did, did they even care?

I just want to make a disclaimer my question wasn't one out of racism on my part, but rather the racism that Native people were subjected to at the time.