What will happen now?
After last-ditch talks failed to reach a resolution on Friday night, members of Congress left Capitol Hill but are expected to return on Saturday.
In his video, Mr Trump said "there is nothing" his Republican party can do about the shutdown and said "we need the Democrats to give us their votes" to resolve it.
"Call it a Democrat shutdown, call it whatever you want but we need their help to get this approved," he said, before urging a bipartisan effort.
Mr Trump had earlier suggested Senate majority leader Mitch McConnell should invoke the so-called "nuclear option" to break the impasse.
The option would mean the bill could be approved in the Senate with a simple majority instead of the 60 currently required - bypassing the need for bipartisan support.