Sen. Bill Cassidy (R-La.) agreed, saying he would prefer to "find another way" to honor McCain.
Cindy McCain was supported by her sons Jack (L) and Jimmy (R) at the service.
And Senator Susan Collins, who many have looked to resist the president's most extreme tendencies, appeared to be uncomfortable when his torch was offered to her. McCain died of brain cancer last Saturday at age 81.
John McCain during a viewing at the Arizona Capitol, Aug. 29, 2018, in Phoenix.
Barry and Linda Vittori separately made the roughly five-hour drive Tuesday night.
"I appreciate what he did for us ... and I'm going to do this for him as long as I can", Costalez said.
"Who would want to vote against naming a building after somebody who just passed away?"
Francis Rodgers, 64, extended a cross-country road trip by two days to be in Phoenix to pay tribute.
"I'd like to put together an official group that can collaborate and bring together ideas from current members, former colleagues and friends", McConnell said on the Senate floor. Wednesday would have been his 82nd birthday.
Cindy admitted her "heart is broken" in a moving message on Twitter following her husband's death, and wrote: "My heart is broken".
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"Decades to come, everyone who came to Washington would know the very special place that John McCain held ... and will continue to hold", she tweeted.
"Imagining an Arizona without John McCain is like picturing Arizona without the Grand Canyon", Ducey said.
"I've been with Senator McCain all around the world and I will tell you that he had better instincts about how and when and where to assert American power than any other leader I've known", Kyl said.
Sen. Jeff Flake gave a benediction at the ceremony. Members of the public in Arizona will later be able to pay their respects. Black curtains hung in the rotunda.
It's worth noting that after about 17 years, over $1 trillion spent, some 2,350 USA troops killed, more than 20,000 wounded, and the untold cost of related medical care and disability pensions, perhaps it was staying in Afghanistan that blew up in our face. She said she liked how McCain didn't act as though he was above others, and she praised all he did for veterans. They said that their hero was a rapper and that upset me. "So, I was really taken aback by it".
Judith Hatch, a veteran from Phoenix, started the day by handing out flags to those who were assembled.
"This man was trusted and he was tested, quality in increasingly short supply", said Ducey.
For some Arizona residents, McCain has been a political fixture in the state for their entire lives.
Arizona Cardinals Pro Bowl wide receiver Larry Fitzgerald will be one of six speakers and one of three athletes participating in Senator John McCain's memorial service in Phoenix on Thursday, according to reports.
A further memorial service will be held on Saturday at the Washington National Cathedral followed by a private memorial service and burial on Sunday at the US Naval Academy in Annapolis, Maryland, where he graduated as a US Navy officer in 1958 before becoming a fighter pilot. Musical choices include a performance of "Amazing Grace" by the Brophy Student Ensemble and a recessional to "My Way" by Frank Sinatra.
Arizona's first responders lined the plaza as the Arizona National Guard team carried McCain inside the Capitol.