A Bush spokesman tweeted a photo of Sully on Sunday as the dog appeared to take a nap beside the late president's casket in a different location, prompting a flood of goodwill toward the service animal.
"His example will always inspire, and his lifetime of service will be enshrined in the hearts of the American people forever", said Vice President Mike Pence.
Senate Majority Leader Mitch McConnell and Senate Minority Leader Chuck Schumer stood side-by-side as a wreath was placed alongside the casket.
As official Washington paid its respects inside the Capitol, Americans queued up outside the Capitol Visitor Center for their chance.
Friends, family and members of the public are gathering across the country this week to remember former President George H.W. Bush.
Both the House and Senate shut down most business on Monday, with lawmakers quickly passing resolutions to allow Mr. Bush to lie in state in the Rotunda, and to use the catafalque, or funeral bier, that was first constructed to hold President Abraham Lincoln's casket in 1865.
Melania represented the current White House. On Wednesday, family and friends will gather at the National Cathedral in Washington for an 11 a.m ET memorial service.
In an invocation opening Monday evening's ceremony, the U.S. House chaplain, the Rev. Patrick J Conroy, praised Bush's commitment to public service, from Navy pilot to congressman, United Nations ambassador, envoy to China and then Central Intelligence Agency director before being elected vice president and then president.
Retired Sen. Bob Dole, of Kansas, who was once Bush's rival for the presidency also paid his respects.
"I think it's night and day", said Sheila Murray, 58, from Stevensville, Maryland, who came with her 14-year-old son, Thomas.
After services in Washington, Bush will be returned to Houston to lie in repose at St. Martin's Episcopal Church before burial Thursday at his family plot on the library grounds. He will be buried alongside Barbara Bush, his wife of 73 years who died in April.
CNN used the event to assume the worst of the president and proceeded not to focus on remembering the life of Bush, but instead focus on attacking the president, more specifically, his character.
National days of mourning don't happen often, so you may be confused about what's open and what's not.