President Biden on Thursday proposed devoting $100 billion in his $1.85 trillion domestic policy bill to protect millions of undocumented immigrants, pushing to salvage a broader immigration overhaul that has stalled in Congress.

Democrats’ efforts to allow such measures to piggyback on the social safety net and climate legislation have so far fallen short, because of strict budget rules that limit what can be included.

House Democrats are planning to try to include one anyway, to appease colleagues who have said they cannot support a plan that lacks help for undocumented people, and to buy themselves time to devise an alternative that might be able to survive the Senate’s arcane rules.

Mr. Biden’s plan would recapture hundreds of thousands of unused visas dating back to 1992 and protect millions of undocumented immigrants who have lived in the United States for years from deportation. It also includes $2.8 billion for U.S. Citizenship and Immigration Services to more efficiently process migrants’ paperwork.

The Senate parliamentarian, the chamber’s top rules enforcer, has repeatedly shot down Democrats’ efforts to include such measures in the bill, which is moving through Congress under a special process known as reconciliation that shields it from a filibuster. Only provisions that directly impact government revenues can be included in such bills, and the parliamentarian has ruled that two other immigration measures do not pass that test.

House Democrats plan to include one of those disqualified plans in their bill: a date change to the immigration registry, which allows otherwise law-abiding undocumented immigrants who have been in the United States continuously since Jan. 1, 2011, to adjust their status and gain a pathway to citizenship.

They fully expect that the provision will be nixed by the parliamentarian, who has said the policy change far outweighed its fiscal impact. They plan to replace it later with a proposal costing about the same amount, once they find an alternative that can survive under Senate rules.

Senate Democrats have embraced a backup plan to expand the Homeland Security secretary’s authority to grant a temporary status known as parole to undocumented immigrants who have lived in the country for a decade, providing them with work permits and shielding them from deportation. The work permits would last five years, and then would need to be renewed for another five. The parliamentarian has not yet ruled on that proposal.

Immigration advocates cheered Mr. Biden’s decision to insist that an immigration overhaul be included in the reconciliation package as evidence they could achieve some aspects of reform while Democrats hold both chambers of Congress and the presidency.

“One way or another, we expect immigration reform to be in the final bill and win freedom for millions of immigrants,” said Lorella Praeli, co-president of Community Change Action.

The Biden administration has already made policy changes to immigration enforcement priorities that would make most of the people eligible for relief in the budget proposals a low priority for arrest and deportation. But those measures are far from permanent and can be reversed by another president.

Eileen Sullivan contributed reporting.