US Senate Majority Leader Sen. Mitch McConnell (left) and Senate Minority Leader Chuck Schumer (Right)
CNN  — 

Bipartisan Senate leaders were upbeat Tuesday that a deal to raise budget caps is within reach, a potentially key breakthrough needed to resolve long-term government funding needs, though it’s unclear if comments President Donald Trump made saying he’d “love to see a shutdown” would harm negotiations.

Senate Majority Leader Mitch McConnell and Senate Minority Leader Chuck Schumer huddled in the Kentucky Republican’s office to hash out remaining differences over the caps, which are the result of the unpopular budget sequestration of 2013, which significantly curbed spending growth on defense and domestic programs.

Such a deal could be completed and voted on by the Thursday deadline to avert a government shutdown and could unblock several long stalled issues in Congress, including increases to defense spending and domestic programs. But doing so would largely be giving up the central component of their leverage to force an immigration deal – the Republican desire to substantially increase defense spending.

Democrats and Republicans rail against the spending restraints but have struggled to reach an agreement to remove them largely because Republicans want to increase Pentagon funding more than domestic funding, something Democrats refuse to do.

As negotiations continue, the exact timing and framework of such a deal remain fluid. In order to be addressed before Thursday government shutdown, the Senate would have to attach the components of the deal to a continuing resolution and send it back to the House (the House is expected to vote on the resolution Tuesday, but increases in defense spending the House is including are expected to be stripped out, meaning the chamber would have to vote again). The House would then have to vote again – and would need significant Democratic support due to pockets of GOP resistance to major spending increases. That has been up in the air, but sources are growing confident the votes would be there.

“We’re on track,” one source told CNN. “Not there yet and there are a lot of technical details to lock in, but we’re on track.”

However, several Republican aides working on the budget deal have voiced concern to CNN that the President’s comments about a shutdown may cause things to fall apart.

“Holding my breath right now,” texted one senior Republican working on the deal.

The issue is whether House Democrats – who have for months been outright resistant to signing onto a budget agreement without a resolution on DACA in sight and are still wary of the current negotiations – will now back away from the breakthrough deal negotiators are approaching.

The President’s remarks happened at the same time McConnell and Schumer, in separate news conferences, touted the progress on the talks and made clear a deal was close. The talks also separate the issue from immigration altogether – long the GOP goal – making the President’s comments somewhat nonsensical.

“I’m very pleased to report my meeting with Sen. McConnell went very well,” Schumer told reporters. “We’re making real progress on a spending deal that would increase caps for both military and middle-class priorities on the domestic side that Democrats have been fighting for. … We are really making good progress.”

“Sen. Schumer and I had a good meeting this morning on a caps deal and the other issues we’ve been discussing for some months now,” McConnell said. “I’m optimistic that very soon we’ll be able to reach an agreement.”

An agreement on the caps would make it much easier for appropriators to reach a funding agreement that will last until a new fiscal year begins October 1. Congress has passed a series of continuing resolutions, or CRs, to keep the government open, except for one brief closure when Democrats resisted approving a stopgap bill to press for unrelated immigration reforms. Overall, those resolutions are considered by both parties to be a clumsy and inefficient way to fund the government because it just continues spending levels from the previous year and makes no needed fine print adjustments for evolving needs at the federal agencies.

“Things are in a good place, but also fragile,” a GOP aide said, noting all of the moving parts in the talks. “We could do without anything inflammatory for a couple of days.”

An agreement could also make it easier to pass other key measures, including overdue disaster relief and a hike in the debt ceiling.

“I know there continues to be discussions on the spending caps and I’m hoping that dam will break and we can get a lot of this overdue business taken care of,” Sen. John Cornyn of Texas, the second-ranking Senate Republican.

Cornyn said he didn’t know how long it would take to process a deal on the caps but indicated at least one more short term CR would need to pass for it to happen. The House is voting Tuesday on a six-week CR that includes a full year of funding for the military.

Senate Democrat are expected to block that bill, meaning Senate leaders will likely have to strip out the extra defense funds and likely send it back to the House before Thursday’s deadline.