 -- White House Deputy Chief of Staff Rick Dearborn said the Trump administration has its work cut out for it to push the GOP health care plan through the Senate, where Republicans hold a slim majority but several members are already wary of the House plan.

"The Senate is a much different animal," Dearborn told ABC News' Political Director Rick Klein and Chief White House Correspondent Jonathan Karl on the "Powerhouse Politics" podcast. "In the House, you can work with the leadership and with leaders of different factions to move lots of members.

"In the Senate, it's much more of a personal relationship with each one of the senators. ... They tend to look at these items a little bit more globally as well. We do have our work cut out for us, but I think we have good foundation and a good base."

Still, Dearborn said the Senate would not be starting over on the health care bill, which some Senate officials have indicated they plan to do.

"I don't think there's a start from scratch," he said. "Will there be some changes? Of course, the Senate is a different animal than the House. But I think we feel really good where we are. There's a proposal that will now go the Senate. We'll work with Senate leadership and the committee chairmen and the rank and file."

The plan passed through the House on Thursday by just a razor-thin margin -- with one vote to spare.

President Donald Trump had the GOP House caucus over to the White House for a lengthy press conference from the Rose Garden to celebrate the bill's passage -- an event usually reserved for a signing ceremony for a bill that is about to become law. But Dearborn also disputed the characterization that the White House had a "celebration" after that vote.

"I don't think that there was a celebration or any kind of a spiking of the football," Dearborn said. "I think that's a narrative that people are trying to build. ... I think it was the president thanking the House for the hard work that they put in. It's not easy. I mean that's a lot of folks that you have to wrangle together. There's a lot of different factions that had to come together."

Dearborn also said Trump supported House GOP members who may be vulnerable in 2018 because of their votes -- and the president is planning on traveling around the country to tout his health care plan.

"I think he's very supportive of those who have supported him on his proposal," he said. "I think he's looking forward ... to getting out and getting his agenda outside the beltway, going to the folks across the country. We've done a little bit of that travel. We'll be doing more of it, and he can have a chance to walk through the successful plan that will ultimately wind up passing the Senate and he'll have a chance to sign when it comes across his desk."