But they are furious with another GOP colleague, Rep. Darrell Issa (Calif.), who has criticized the relief bill, claiming it is filled with wasteful spending.
"That's just not accurate," Grimm said on CNN's "Starting Point" of Issa's claims. "There will be no pork in this bill."
"He is 1,000 percent wrong," King said of the California lawmaker, in a separate interview, also on CNN. King said the disaster-relief requests include only what the governors of the states affected by Sandy requested.
"If he wants to take it up with somebody, call Gov. [Chris] Christie," he added, referring to New Jersey's Republican governor.
Issa told Fox News on Wednesday that the Senate added unneeded funding requests to the bill. He defended Boehner for delaying the House vote because the Senate had already left town.
Boehner on Tuesday night canceled plans to hold votes on the Sandy bill, angering lawmakers from the affected states. King was so furious at the delay that he suggested early Wednesday that he might not support Boehner as Speaker.
Representatives from New York and New Jersey met with House leadership on Wednesday afternoon to express their dismay with the Speaker's decision and urge Boehner to bring votes to the floor as quickly as possible after the new Congress begins on Thursday.
Boehner decided to schedule two votes, with the House taking up a measure for $9 billion to shore up the National Flood Insurance Program on Friday and another $51 billion Sandy spending package on Jan. 15.
Grimm and King on Thursday said they are content with Boehner's response.
"I did stay behind after the conference to speak one-on-one with the Speaker and the [majority] leader, [Eric Cantor (R-Va.)] to shake his hand and look him in the eyes," Grimm told CNN. He said he wanted to ensure that the House would have the chance to vote on the full $63 billion requested for disaster relief in the region.
"I got his commitment and his word as a man and I feel pretty comfortable with that," Grimm said.
King, who appeared on multiple networks Thursday morning to praise Boehner's quick response to criticism, described a similar meeting with Boehner the previous day.
"The bottom line is that ultimately we got what we wanted," he told CNN. "As far as I'm concerned, it's over with. John Boehner and I have been friends before; hopefully we're friends again. We shook hands yesterday."
But New Jersey Democratic Rep. Frank Pallone Jr. told CNN that Boehner's actions were "not enough."
“I really think that the Speaker doesn't care about New York and New Jersey," Pallone told "Early Start" on Thursday. "In other words, we're blue states. The fact of the matter is that he was afraid to bring this up yesterday, in my opinion, because the Tea Party and the right wing did not want to vote for the spending bill for New York or primarily for New York and New Jersey.”
Grimm and King both defended Boehner's attitude toward disaster relief, and noted that the legislation had been delayed by others since Sandy made landfall in October.
"It was never the case that the Speaker's heart wasn't with New York or didn't want the vote," Grimm said.