(CNN) -- The promise of $60 billion can do a lot to calm outrage.
That point was underscored Wednesday, when House leaders met with irate representatives from New York and New Jersey who felt they had been ignored by House Speaker John Boehner when he scrapped a planned vote late Tuesday on a massive aid package for Superstorm Sandy victims.
"We're getting what New York and New Jersey need, and that's all that counts," Rep. Peter King, R-New York, told reporters after emerging from a 20-minute meeting with Boehner and House Majority Leader Eric Cantor. "We're all big boys; we understand that all that counts is the bottom line."
A vote on $9 billion for immediate aid is now set for Friday, with the balance of $51 billion due for consideration January 15.
For its part, the Senate plans to vote by unanimous consent on Friday on the $9 billion but is waiting to see what is in the larger package before announcing a plan for that, a Senate Democratic leadership aide said.
"On the second tranche, we will need to see more details before we decide how to proceed," the aide said. "As the Senate has shown by passing our bipartisan bill, we consider getting aid to the victims of Sandy a superlative priority, but we need to know more about the contents of the bill before deciding on a path forward."
Democrats were less mollified.
"While it would have been far better had they passed the Senate's bill today, at least this provides a path to produce the needed $60 billion for New York and New Jersey by the end of the month," said Sen. Charles Schumer, D-New York, in a statement.
"It's really unbelievable how Speaker Boehner and his party could just walk away," said Christine Quinn, speaker of the New York City Council. "To promise us a vote weeks from now? Why should we believe him at all? It's just shocking."
In a statement, Boehner and Cantor said "critical aid" to storm victims should be the first priority of the new Congress, which convenes Thursday.
The comity contrasted sharply with the outrage that had exploded earlier in the day over Congress' inaction on the package, pitting even fellow Republicans against Boehner.
It was "disappointing and disgusting to watch," said New Jersey Gov. Chris Christie, blaming "the toxic internal politics of the House majority."
"New Jersey deserves better than the duplicity we saw on display," he said, adding, "shame on Congress."
Christie, a Republican, said he had tried to reach Boehner on Tuesday night after the latter canceled a vote on the aid bill, which had already been approved by the Senate. "He did not take my calls," said Christie.
In a news conference, Christie said he joined people of his state in feeling "betrayed" and added that the move summarizes "why the American people hate Congress."
In a statement, Christie and New York Gov. Andrew Cuomo wrote: "This failure to come to the aid of Americans following a severe and devastating natural disaster is unprecedented. The fact that days continue to go by while people suffer, families are out of their homes, and men and women remain jobless and struggling during these harsh winter months is a dereliction of duty. "
Boehner did not make public remarks and did not post about the issue on social media.
GOP leadership sources said Boehner was worried it would be a bad political move for him to allow a vote on the new federal spending after a long day of getting pummeled by his own House Republicans for not demanding enough spending cuts in the fiscal cliff bill.
Civility was restored late in the afternoon. "As far as I'm concerned, that was a lifetime ago," King said. "I know it was last night, but the bottom line is we're going forward getting what we believe is necessary."
Earlier, King had slammed his own party. "The Republican Party has said it's the party of 'family values.' Last night, it turned its back on the most essential value of all, and that's to provide food, shelter, clothing and relief for people who have been hit by a natural disaster," King told CNN.
King said he chased Boehner "all over the House last night" and that Boehner had said everything would be taken care of after the vote on the fiscal cliff. But Boehner left.
King called the House leadership's move a "knife in the back."
"Anyone from New York or New Jersey who contributes one penny to the Republican Congressional Campaign Committee should have their head examined," King said. It's very rare for a lawmaker to call on anyone not to support his own party.
But on Wednesday afternoon, King said he would vote for Boehner in leadership elections scheduled for Thursday.
A senior GOP leadership aide said Boehner will make a Sandy aid package "his first priority in the new Congress," which begins its term Thursday.
When a new Congress begins, both chambers have to begin from scratch with legislation, so the Senate's passage of a previous bill will be moot.
Michael Steel, Boehner's spokesman, said the speaker is "committed to getting this bill passed this month."
Before the House adjourned Wednesday, President Barack Obama urged a vote.
"It has only been two months since Hurricane Sandy devastated communities across New York, New Jersey, and Connecticut as well as other Eastern states. Our citizens are still trying to put their lives back together," Obama said in a statement.
"When tragedy strikes, Americans come together to support those in need. I urge Republicans in the House of Representatives to do the same, bring this important request to a vote today, and pass it without delay for our fellow Americans," Obama said.
Some of the harshest comments came from King.
Scott Mandel, vice president of New York's Long Beach City Council, told CNN, "The money was needed yesterday, and the fact that there's an obstacle in the way for whatever reason and a vote wasn't allowed to go forward was inexcusable."
The money would improve the city's ability to withstand damage from winter storms, Mandel said.
Fiscal cliff battle held up the measure
The tumultuous process of getting the fiscal cliff deal passed in the House had held up the relief measure, and many House Republicans opposed the size of the Senate bill.
"Leadership was all-consumed with the cliff procedure," Rogers told reporters off the House floor late Tuesday. "And they really have not had the time to devote to this because of that."
Sandy killed at least 113 people in the United States and left millions of people without power after running up the East Coast in late October. The storm hit hardest in New York and New Jersey.
Cuomo has put storm-related costs at $41.9 billion, while Christie has estimated a price tag of $36.8 billion.
The bill includes grant funding for owners of homes and businesses, as well as funding for public improvement projects on the electrical grid, hospitals and transit systems to prevent damage from future storms.
John Stone, a resident of New York's Staten Island, owned two homes before the storm. One was destroyed; the other was so severely flooded that it remains unlivable.
But he expressed no anger over the House's decision. "They'll just have to do it all over again, I suppose. What can you say?"
"It's a lot of money," he said, adding "there's a lot of other things they've got to do."
He tends to vote Republican and doesn't plan to turn away from the party, he said, although, he added, "I don't give them much money anyway."
He's been living with relatives in New Jersey.
CNN's Lesa Desjardins, Victor Blackwell, Deirdre Walsh, Steve Kastenbaum and Dan Merica contributed to this report.