(CNN) Republican members of Congress made their way back Wednesday morning to the Capitol still in the baseball clothes they'd been wearing when gunfire broke out at their practice field in a Virginia suburb.

But members' response to the shooting came down to one goal: unity.

In a Capitol building that is typically full of partisan rancor, the mood was somber and quiet Wednesday. Votes were canceled in the House of Representatives as members waited anxiously to get more news on Scalise's condition. The Democratic Whip Steny Hoyer's staff delivered pizza to Scalise's office in the late afternoon. The Democratic baseball team invited the Republican team to the Democratic Club Wednesday night for dinner.

Throughout the day, those House Republicans who were targeted at baseball practice were greeted with warm embraces and back slaps from fellow members on both sides of the aisle.

Ohio Rep Brad Wenstrup, on his way to do a TV interview with CNN, gave a bear hug to Georgia Rep. Doug Collins in the hallway. Texas Republican Rep. Joe Barton, the manager of the Republicans' team, recalled in an emotional news conference that his son was "at practice this morning, and he had 25 dads." Rep. Mike Doyle, the Democratic baseball manager, touched Barton's arm at the podium to console him.

When the House convened briefly at noon, members filed in and took their seats. On most days, members wouldn't go to the floor unless they were speaking, but on Wednesday the chamber was full. Members walked over to those Republican lawmakers who witnessed the attack and checked in on them. Members on both sides of the chamber listened intently to the comments by both House Speaker Paul Ryan and House Minority Leader Nancy Pelosi. Many praised the message of unity, and the appreciation the entire congressional community feels for the Capitol Police.

On the Senate side, Republican Majority Leader Mitch McConnell and Minority Leader Chuck Schumer skipped their usual partisan opening speeches, and instead admonished the horrific attack and thanked the Capitol Police officers who saved lives on the field.

"There are no D's and R's behind our names today," Rep. Joe Crowley, a Democrat from New York, said.

Members were visibly shaken by the events of Wednesday morning. Many Democrats and Republicans refrained from politicizing the attack or casting it as a referendum on the Second Amendment. Instead, they said the incident caused them to reflect on how the country might heal and come together after a contentious election and first few months of the Trump administration.

"I'm hopeful today's events create an opportunity for all Americans to stop and think about the level of political discourse in this country," said Rep. Richard Hudson, a Republican from North Carolina who had been on his way to bible study when he heard the news.

Hudson said that he was touched by a post in an Indivisible Facebook group -- a group that aligns itself with Democrats -- that celebrated that he was safe.

"That really meant a lot to me," he said.

In a closed-door, all-member House briefing Wednesday morning, Rep. Al Green, a Democrat from Texas who has called for Trump's impeachment on the House floor, rose to say "an attack on one is an attack on all."

For many members, the men's baseball and women's softball teams had become a rare opportunity to break away from partisan lines in recent months.

"What makes it even more awful is this is one of the things that's right with this town. This is a game where Republicans and Democrats come together and put fellowship and bipartisanship ahead of party politics," said Democratic Sen. Chris Murphy. "I know Steve Scalise because of this baseball game. For eight years, I've been the catcher bantering with Steve Scalise when he comes up to bat a few times a game."

"I mean, I've only been in Congress for 10 years and I've had two of my friends shot," Murphy added. "I don't think you're human if that doesn't shake you."

Panic on the field

The timeline of the morning's event had been recounted over and over again. Members told stories of their colleagues coming to their side.

Wenstrup, who is an Iraq war veteran and medic, jumped into the dugout when he heard Rep. Trent Kelly, of Mississippi, another veteran, yell "shooter" Wednesday morning. Wenstrup treated Scalise at the scene and told CNN he was concerned about the majority whip. He had found an entry wound for the bullet, but couldn't find the exit wound, and was concerned about internal injuries. He said Scalise was conscious, answering questions, and asked for water. He said that he and his GOP colleagues had felt hopeless as the gunfire continued and they saw Scalise alone and hit out on the field. They were unable to get to him for several minutes.

GOP Shooting Map Illustration

Rep. Chuck Fleischmann retold the story to reporters off the floor of how members huddled down in the dugout waiting for the gunshots to end.

"We were scared because when the gunfire didn't stop we thought, 'Oh my gosh he's gonna come in there and we're like sitting ducks,'" Fleishmann said. "It was chaotic and afterwards it was very sad because there were so many people injured."

How to move forward

The congressional baseball game and the women's press vs. member softball game will go on at the behest of members who don't want to let Wednesday's shooting shatter their bridge to bipartisanship.

But Wednesday, members were still grappling with how to move forward.

"You become numb to this until something like this happens," said Rep. Lou Baretta, a Pennsylvania Republican. "It's the reality check that this is the world we live in today. It's very easy targets."

Lawmakers and their staffs said Wednesday's shooting once again exposed a reality that they are vulnerable targets anytime they leave the security of the Capitol. Many pondered security changes that could be in store, but most acknowledged it was not feasible to give all 535 lawmakers on Capitol Hill a security detail.

"People think members have security," Virginia Democratic Sen. Tim Kaine said. "We have wonderful security on the Hill, but anytime we're off, we don't. So it's very sobering, and I'm sure we'll have to grapple with it."

Some were already contemplating what changes could be made, a subject Sen. Rand Paul -- who was on the field at Wednesday's shooting -- said he's been thinking about since the Charlie Hebdo attacks in France in 2015.

"I think we will make some proposals and changes," the Kentucky Republican told reporters. "About a year ago I got interested in Charlie Hebdo, I've been promoting these changes around here, some changes to our entrances. I have been interested in it. With this latest attack, I think we're going to redouble our efforts to look at security."

Sen. David Perdue suggested that perhaps police should be present for groups of lawmakers gathering outside the Capitol, but he argued it was important for Congress not to wall itself off from the public.

"I don't think you want to build a barrier between individuals and their constituents or individuals and the public," Perdue said. "That's not America. So, it's one of the risks you take on."