Trump has said he'd be "proud" to have a shutdown over the $5 billion he wants for the wall on the U.S.-Mexico border.
Asked Sunday if there was room for compromise, Schumer told NBC: "He's not going to get the wall in any form."
Schumer and House Minority Leader Nancy Pelosi have proposed no more than $1.6 billion. The money would not go for the wall but for fencing upgrades and other border security. Democrats also offered to keep funding at its current level, $1.3 billion.
Schumer says Trump doesn't have the votes from the Republican-controlled Congress to support $5 billion for the wall.