By Susan Cornwell

WASHINGTON (Reuters) - Democrats in the U.S. Congress were scrambling on Monday to find another way to include immigration reform in a sweeping $3.5 trillion social spending bill after a Senate arbiter said their first proposal broke the chamber's rules.

The ruling was the latest in a series of stumbling blocks President Joe Biden's party faces as it enters a critical few weeks before a Sept. 27 vote on a $1 trillion Senate-approved infrastructure bill. Also ahead is an Oct. 1 deadline to continue funding the federal government and the threat later in the month that the government will breach its borrowing cap, risking default on U.S. payment obligations.

Democrats can afford to lose just three votes in the House of Representatives and none in the Senate if they are to pass the packages. But the party's moderate and progressive factions are at odds over the size of the $3.5 trillion program, which includes proposals for childcare, education, housing and green energy.

Progressives insist on passing the $1 trillion infrastructure bill and the $3.5 trillion measure in tandem, with some threatening to vote against the smaller bill otherwise.

Moderates note the larger bill has not even been written yet, and have secured an agreement from House Speaker Nancy Pelosi to vote on the smaller bipartisan bill next week.

Representative James Clyburn, the third-ranking House Democrat, on Sunday acknowledged the larger bill may need to be trimmed to pass.

One possible compromise would be to vote on the infrastructure bill as scheduled on Sept. 27 but for Pelosi not to forward it to Biden to sign until the larger package passes.

One moderate House Republican on Monday signaled he would vote for the smaller bill if it came up by itself.

"Representative (Don) Bacon plans to vote 'yes' for the bipartisan infrastructure bill, as long as it is not coupled with the $3.5 trillion spending bill," said Danielle Jensen, a spokeswoman for Bacon.

? Moderate Senate Democrats including Joe Manchin and Kyrsten Sinema say $3.5 trillion is too much; Manchin suggests spending less than half that.

To get the bill passed in the Senate, Democrats plan to use a maneuver called budget "reconciliation" to avoid the requirement for 60 votes in the 100-member chamber.

But they suffered a setback on Sunday when the Senate parliamentarian ruled that a provision giving a path to citizenship for millions of immigrants, including the so-called Dreamers brought to the United States as children, could not be included under the Senate rules.

Senate Majority Leader Chuck Schumer said Democrats would pursue alternatives.

Senator Robert Menendez said on Monday one alternative would be to try to bring the date of arrival in the United States for eligibility for legal status for some immigrants forward from the current Jan. 1, 1972.

"We're not going to take no for an answer," Menendez said in a conference call with reporters.

DEBT CEILING

While the Sept. 27 deadline is self-imposed, two more rigid ones come next.

The first is Oct. 1, when funding for government operations runs out, which would force the stoppage of many federal functions as has happened three times in the past decade.

In addition, U.S. Treasury Secretary Janet Yellen has warned that sometime in October the Treasury will exhaust its cash reserves and borrowing capacity under the $28.4 trillion federal debt limit, and be unable to pay all of its bills or service its debt without congressional action to raise the limit.

Pelosi and Schumer packaged the two issues into one bill on Monday, saying legislation to avoid a government shutdown by funding the government through the end of this year will also include a suspension of the debt ceiling through December 2022. The bill is coming before the House this week.

A U.S. default would roil financial markets, lead to cuts in services and benefits and hit the nation's credit rating. It could also plunge the economy back into recession.

Senate Republican Leader Mitch McConnell and other top Republicans have warned they will not vote to boost the national debt limit, despite having done so repeatedly when Republican Donald Trump was president.

(Reporting by Susan Cornwell; Additional reporting by David Morgan; Editing by Scott Malone and Sonya Hepinstall)