WASHINGTON (CNN) -- As proponents of gun control legislation in the Senate struggle to get enough votes for their bill, former Rep. Gabrielle Giffords and her husband, Mark Kelly, say they feel "optimistic" that the bipartisan compromise will get enough approval.
And Sen. Joe Manchin, D-West Virginia indicated the bill could potentially be tweaked to convince opponents to join their side, while Vice President Joe Biden said advocates are "working" to get the 60 votes needed to pass.
"We are optimistic that this can pass," Kelly told CNN, after walking through the Capitol Tuesday with Manchin and Sen. Pat Toomey, R-Pennsylvania.
Toomey and Manchin are the two architects of an agreement that would expand the background check system to include firearm sales at gun shows and over the internet.
The Senate is expected to take up a package of gun proposals this week, starting with the Manchin-Toomey amendment. The overall gun bill also contains measures to crack down on gun trafficking and straw purchases, as well as finding ways to improve school safety.
The compromise deal, reached last week and originally thought to make it through the Senate, is now trying to stay above water, as several Republican senators have indicated they plan to oppose the measure.
As the group--Manchin, Toomey, Kelly and Giffords--was walking into an elevator Tuesday, one reporter asked if the senators are considering a possible change to the legislation, which would allow exemptions for rural gun owners who have to travel far to purchase a gun. Such a measure could help sway senators from states like Alaska.
Responding, Manchin suggested a change could be made.
"We're looking at everything that really makes sense," he said. "We're looking at everything that could be of more help."
Asked if he's optimistic about a bill getting through the Senate, he replied with a smile: "Always optimistic."
Biden was also on the Hill Tuesday for a ceremony dedicating a room to Gabe Zimmerman, a congressional aide who lost his life in the same Tucson shooting that wounded Giffords.
"I think we're going to be OK," Biden told reporters when asked about the gun bill in the Senate.
But, the former senator from Delaware added, he's "learned after 36 years not to predict what the Senate's going to do on anything."
Asked if he's talking to certain senators who are on the fence about the bill, Biden said: "I'm just reaching out to my friends."
"We are working to get to 60 and it's fluid. I think we're there, but it's not unusual as you all know for people to make up their minds at the last minute," he said. "But we'll see."
Despite the obstacles ahead, Kelly also said they're hopeful the bill can get enough support. Kelly and Giffords, who was shot in the head more than two years ago, have been vocal advocates in the renewed campaign to combat gun violence.
"I think there's a good chance," Kelly said. "It's going to take a little work. That's why Gabby and I are here. And ya know I think we'll get this done."
Read more: 'Stronger, better, tougher:' Giffords improves, but she'll never be the same
Republican Sens. Saxby Chambliss of Georgia, Roger Wicker of Mississippi, and Richard Burr of North Carolina told CNN Monday of their plans to vote against the measure, while Sen. Jeff Flake of Arizona announced his decision on his Facebook page the same night.
On the other hand, four Republicans have voiced support or said they were leaning in favor of supporting the amendment. With at least two moderate Democrats from pro-gun states known to oppose the measure, it needs at least seven GOP votes to have any chance of passing.
Manchin told CNN on Monday a vote on his amendment would be pushed back to try and build more support in order to get the 60 votes that are effectively needed for passage.
Asked if the vote would take place Tuesday or Wednesday, as supporters had hoped, Manchin said he didn't think so.
"I would say by the end of the week, probably," he added.