Despite Shelby's confidence, it is unclear whether Trump will back an agreement lawmakers reach. The president has repeatedly pushed for Congress to approve $5.7 billion to build his proposed border wall. Democrats have refused, but shown willingness to pass funds for other security measures such as technology, more personnel or repairing existing fencing.
Congressional leaders are rushing to avoid a partial government closure, after the wall dispute led to a record 35-day lapse in funding in parts of December and January. Top Republicans and Democrats have shown no appetite for another shutdown, even as Trump threatens to let funding lapse again. He has also warned that he could declare a national emergency to build the barrier without congressional approval — a move that numerous Senate Republicans oppose.
A White House spokesman did not immediately respond to a request to comment on the progress of talks and what the president would accept in a deal. Still, Congress appeared optimistic Thursday as negotiations on the bipartisan, bicameral conference committee continue.
Senate Appropriations Committee Vice Chairman Patrick Leahy, D-Vt., believes a deal "can be reached" as talks are still ongoing, according to his spokesman Jay Tilton. Meanwhile, a House Democratic aide said crafting a deal by Monday is feasible, adding that the negotiators want to strike an agreement "as quickly as possible."
Congressional leaders clearly want to avoid another lapse in funding. The last closure led to 800,000 federal workers missing two paychecks and disrupted various government services. Voters largely pinned the blame for it on Trump, according to opinion polls.
On Wednesday, House Speaker Nancy Pelosi told Politico flatly: "There will not be another shutdown." She said Thursday that she has "confidence" in the lawmakers in charge of appropriations.
Senate Majority Leader Mitch McConnell has also warned Trump against another shutdown.
WATCH: What Republicans want to avoid another shutdown