WASHINGTON — House Minority Leader Nancy Pelosi said Wednesday she couldn’t support a broad spending deal that would keep the government open and meet most Democratic demands unless House Republicans allow votes on legislation to help young immigrants, throwing GOP efforts to avoid another government shutdown into turmoil.

House Speaker Paul Ryan, R-Wis., will almost surely need Democratic votes to pass a two-year spending bill now before the Senate, which would raise both military and domestic spending caps and include long-delayed disaster funding for last fall’s hurricanes and the Wine Country fires.

Mounting an extraordinary one-woman filibuster on the House floor beginning at 10 a.m. EST, Pelosi used her leadership prerogative, known as “the magic minute,” to hold the House floor for going on two hours, reading stories about the lives of undocumented immigrants who arrived in the U.S. before they were 16. They have been protected from deportation under an Obama administration program called Deferred Action for Childhood Arrivals, or DACA, that President Trump intends to end as of March 5.

“Maybe we should just pray all day,” the San Francisco Democrat said at one point, suggesting she should bring her rosaries — blessed by Pope Francis and other popes before him — and quoting St. Augustine’s admonition that “any government not formed to promote justice is just a bunch of thieves.”

Pelosi issued a statement Wednesday morning saying the two-year budget agreement reached in bipartisan Senate negotiations includes “many Democratic priorities” that she and Senate Democratic Leader Chuck Schumer of New York have been demanding for months.

The Senate deal would raise spending by $300 billion over the next two years and extend the Children’s Health Insurance Program for a decade. More than half the additional money, $165 billion, would go to the military, and $131 billion to domestic programs.

The conservative House Freedom Caucus favors the increase in defense spending but objects to the higher domestic spending on the grounds that it would add to the deficit. As a result, Republican leaders are likely to need Democratic votes to help pass the measure in the House.

“Democrats have secured hundreds of billions of dollars to invest in communities across America,” Pelosi said, referring to the Senate deal. “There will be billions in funding to fight opioids, to strengthen our veterans and the (National Institutes of Health), to build job-creating rural infrastructure and broadband, and to fund access to child care and quality higher education.”

But Pelosi said a morning caucus of House Democrats concluded that the package “does nothing to advance bipartisan legislation to protect Dreamers,” referring to DACA recipients. “Without a commitment from Speaker Ryan comparable to the commitment from Leader McConnell, this package does not have my support.”

Senate Majority Leader Mitch McConnell, R-Ky., reiterated his promise Wednesday to hold an open Senate debate on immigration, a promise that if carried out would allow a Democratic-backed bill to pass with some GOP support.

None of the spending bills before Congress includes immigration legislation. Pelosi and House Democrats are demanding that the House be allowed to consider Democratic-backed immigration bills, as McConnell has promised the Senate will.

The commitment Pelosi is demanding from Ryan would open the House to a full debate on immigration legislation, where a bill that protects DACA recipients but does not include White House demands to build a wall on the southern border and restrict legal immigration would stand a good chance of passing, with the support of a vast majority of Democratic votes and a minority of Republicans.

Ryan said Tuesday he would not bring an immigration bill to the House floor that lacks support from a majority of Republicans and the White House. His spokeswoman reiterated that position Wednesday.

Carolyn Lochhead is The San Francisco Chronicle’s Washington correspondent. Email: clochhead@sfchronicle.com