A draft U.S. Senate spending bill includes $56 million to continue construction of the new Department of Homeland Security headquarters at the former St. Elizabeths Hospital site in Southeast Washington, setting the stage for a clash with the House on the issue.

The DHS project is designed to consolidate dozens of agencies with thousands of workers scattered at different locations onto one sprawling campus. The Obama administration has requested $160 million for the project, but in June, the House passed its version of the fiscal 2012 Homeland Security bill without including any of the money.

House appropriators said in a report accompanying the bill that they thought the DHS project had been mismanaged and that “both costs and schedule of the current project are matters of concern” to Congress.

But the administration said the funding cut could delay the project by two years, and District officials, including Del. Eleanor Holmes Norton (D-D.C.), and local labor unions have complained that the move could cost thousands of construction jobs.

The Senate bill would give the administration only some of what it wanted — its proposed funding level would allow completion of the Coast Guard headquarters but would not provide money to begin the next phase of construction.

Although Senate Democrats look more favorably on the project than their House Republican counterparts, both chambers face pressure to cut spending across the government.

“We just couldn’t afford it,” said a Senate Appropriations Committee aide who spoke on the condition of anonymity to discuss internal panel decisions. “What we funded is enough to complete the building they’re currently working on.”

The aide said senators hoped more money would be available for the headquarters site next year.

Although the Senate measure does not fully fund the project, Norton said Tuesday that she was pleased by the chamber’s decision.

“ ‘Relieved’ does not express what I felt that this project was not zeroed out,” Norton said. She later added, “If there was any urgency, it was to make sure . . . that first building was completed.”

Most important, Norton said, the Senate’s funding level would ensure that the project would continue to hire construction workers rather than shedding them.

The full Senate Appropriations Committee is expected to approve the spending bill Wednesday. The House and Senate will have to agree on a final version of the Homeland Security bill this year.