The Senate is expected to launch an immigration debate in a matter of days.
"Without a commitment from Speaker Ryan comparable to the commitment from Leader McConnell, this package does not have my support," she said.
Ryan, however, has made no such commitment on Dreamers, stoking concerns that any immigration bill would simply languish in the House.
The immigration debate drove the three-day shutdown last month, as Democrats pushed McConnell to agree to prioritize the issue, but it had not been part of more recent budget negotiations.
Dreamers, the immigrants who came to the U.S. illegally as children, face possible deportation as Trump ends the Deferred Action for Childhood Arrivals program, which has allowed them to apply to live and work here. The program was set to end March 5, but a court challenge is allowing it to continue for now.
Lawmakers in both parties say they want to protect the Dreamers as part of a broader immigration bill that would include border security and perhaps other measures, and they believe a bipartisan deal would easily pass both chambers.
However, Ryan is under pressure from conservatives in his majority to stand by his earlier promise not to consider immigration legislation unless it is supported by most of the House Republican majority.
More recently, Ryan has said he would consider legislation that Trump supports, but the president's own shifting views on immigration have made a legislative deal difficult.
Bipartisan groups in Congress continue to meet to strike a deal as the Senate prepares to open debate next.
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