The Senate Appropriations Committee is likely to skip two of the most controversial annual funding bills, signaling they will save those fights for a larger spending deal or floor votes.

Republicans on the panel say they are hoping to hold committee votes on 10 of the 12 fiscal 2021 government funding bills by the end of June and potentially bring some of those to the floor in June as senators try to get legislation back on track amid the coronavirus pandemic.

"I think we'd have some bills possibly on the floor in June and all of the markups that we're likely to do, which would be at least 10 of them, by the end of June," said Sen. Roy Blunt (R-Mo.), who chairs the Appropriations labor, health and human services and education subcommittee.

Pressed about the timeline, Senate Appropriations Committee Chairman Richard Shelby (R-Ala.) said "that would be a worthy goal. We've all talked about that."

"We'd like to, but I said all of this is tentative at the moment. We've been discussing it amongst ourselves," Shelby added on the possibility of being able to bring some funding bills to the floor for votes in June.

Asked about Blunt's prediction that the committee could vote on 10 of the 12 bills, Shelby confirmed that was the plan "at this point."

"To mark up, we want some understanding that we're going to have some cooperation," Shelby said.

He pointed to the spending bill for the Department of Homeland Security (DHS) and a separate bill on military construction and Veterans Affairs (VA) as the two bills the committee was not planning to bring up.

"[A] bill that might be susceptible to a big political fight over the wall is one," Shelby said, in a reference to the DHS funding bill, when asked what two bills the committee isn't planning to take up.

He confirmed that the second bill not on the agenda was the military construction-VA bill.

The new timeline comes after GOP members of the Senate Appropriations Committee met this week to discuss a path forward on the fiscal 2021 funding bills as the coronavirus has upended the normal legislative schedule on Capitol Hill.

The DHS bill has emerged as a perennial headache for lawmakers because of the fight over President Trump's border wall, with the details over physical barrier funding and restrictions usually one of the last items to get resolved in large spending deals.

But senators also pointed to the growing cost of VA health care as another early hurdle. Overall nondefense spending for fiscal 2021 was agreed to as part of a two-year budget deal, meaning that if senators include more money for the VA without changing the budget cap, they have to strip funding from other nondefense programs.

There is some bipartisan support for treating the extra VA health care costs as "emergency" spending, exempting the funding from the bipartisan budget cap.

"Some of us have advocated we ought to use that as emergency, deem emergency spending. Some people don't want to do that that way. Some do. That debate's going on right now," Shelby told The Hill.

He added in a separate discussion with reporters this week that the VA issue was a "a big problem."

"That probably won't be resolved unless it's resolved at the presidential, leadership level," Shelby said.

Sen. Lisa Murkowski (R-Alaska), another member of the Appropriations Committee, said senators were "dealing with and discussing the challenges that are in front of us with ... a VA account and the additional resources there for the mission."

Lawmakers have until the end of September to approve all 12 appropriations bills or pass a continuing resolution, which would buy them more time to negotiate a larger deal.

Given the ongoing pandemic and the looming election, some are already resigning themselves to the increased likelihood of a continuing resolution.

"I think the timeline would have been delayed anyway because of the election. I'm a subcommittee chairman and I'm going to do my job, but you don't have to be a senior at LSU to figure out that a budget is going to be difficult to pass until after the presidential election," said Sen. John Kennedy (R-La.).