Seventy percent of those surveyed said they supported the death penalty for the 19-year-old, the poll, released Wednesday, said.
Tsarnaev has been charged with using a weapon of mass destruction and malicious destruction of property resulting in death. He is accused, along with his older brother, Tamerlan, of setting off two bombs at the Boston Marathon April 15, killing three people and injuring more than 260.
The support for capital punishment crosses party lines with most people of both the Democratic and Republican parties agreeing at least somewhat.
The bigger divide is racial, with 75 percent of white people said they supported the death penalty, compared to 62 percent of Hispanic people and 52 percent of African-American respondents, the poll said.
The racial division is reflected in the overall support in the death penalty itself, The Washington Post said. A recent Washington Post Maryland poll indicated 63 percent of white respondents and 37 percent of African-Americans asked said they support the death penalty for people convicted of murder.
A random sample of 1,000 adult Americans was surveyed for The Washington Post-ABC News poll from April 24-28. There is a 3.5 percentage point margin of error for the results.