(CNN) President Donald Trump's angry threats Wednesday to not work with congressional Democrats until they stopped investigating him came at a sensitive time for talks over several important issues that bipartisan negotiators on Capitol Hill and the White House had hoped to wrap up before Congress leaves as early as Thursday for the Memorial Day recess.

The sudden "flare up," in the words of one GOP leader, left an air of uncertainly over the talks that all sides had reported upbeat progress on in recent days. It also wasn't clear to lawmakers whether Trump's threat related only to the infrastructure spending proposal -- that was the subject of the meeting with Democrats that Trump stormed out of -- or if it meant all legislation.

"Seems like we have a little bit of an issue right now," said Sen. John Thune of South Dakota, the second-ranking GOP leader. "It's hard to figure how much gets done around here unless the atmospherics change."

White House and congressional negotiators have been working for weeks to resolve differences over an overdue multi-billion-dollar disaster aid package that they appeared to be on the cusp of completing before the dispute. That measure is likely to include billions for the migrant crisis on the southern border, a thorny issue for the parties.

Negotiators are also making steady progress on a broad budget package that could put off the threat of a government shutdown or debt default until after the next election. The top four congressional leaders huddled for hours Tuesday with top White House officials but came up short on a deal.

Lawmakers said they didn't know when those talks might restart -- perhaps this week or maybe after next week's recess once tempers cool.

"Sometimes tempers around here flare and emotions get pretty high but, in the end, we've got work to do. The best thing we can do would be to try to make progress where we can," said Sen. John Cornyn, a Texas Republican when asked if the spat should disrupt bipartisan work on the Hill. "But that was fairly dramatic this morning."

Thune said it was critical that "no matter how bad it is around here" lawmakers find a way to reach a budget and debt ceiling deal and pass disaster aid.

"These are the things that need to get done," he said. "I think it makes all those things a heavier lift when you have this kind of operating environment."

Senate Republican leaders said despite the brouhaha, they were hopeful Democrats who control the House would soon vote on a disaster bill -- even though negotiators were still putting the final touches on it -- so the Senate could take it up possibly Thursday.

Senate Majority Leader Mitch McConnell started his day by announcing the chamber would not recess before "taking further action" on the bill, a gentle threat aimed at prodding negotiations that didn't even include a demand the bill become law before they recessed. McConnell didn't know that an hour later Trump would be in the Rose Garden blasting House Speaker Nancy Pelosi for charging he was involved in a cover up and threatening to stop working with Democrats.

"I taught preschool. I know a temper tantrum when I see it," quipped Sen. Patty Murray, the number three Democratic leader, who was in the meeting with Trump.

"The people of this country expect us to respect and work with each other no matter their differences," she added, noting she had cut deals with Presidents Bill Clinton and Barack Obama when they were under investigation by congressional Republicans and George Bush when he was facing heavy scrutiny over the Iraq war.

Other Republicans were hopeful Trump's threat to hold up legislation would not extend beyond his $2 trillion infrastructure proposal, which many Republicans oppose anyhow because it's expensive and they don't want to raise the gas tax on consumers to pay for it.

Departing a weekly meeting of Senate GOP committee chairs in the Capitol, which took place right after Trump's appearance in the Rose Garden, two senior senators said they didn't expect Trump's threat to have a practical impact on their work.

"I just came from a meeting where there are five bills that we can get up between now and August," said Sen. Chuck Grassley of Iowa, who heads the powerful Finance Committee.

Sen. Susan Collins of Maine said she interpreted his threat to only apply to the infrastructure bill.

"We were just discussing in the chairmen's meeting the number of bipartisan initiatives that could come to the floor and I think the President's comments really are referring to infrastructure," she said.

Collins, who is up for reelection, pointed to a series of issues the health and finance committees are dealing with to reduce health care costs -- prescription drugs costs, in particular. She said she looks forward to the Senate returning to a "fuller legislative agenda" after clearing out a "backlog of nominations," which she said she expects to happen.

Also, in that meeting was McConnell who declined to comment on the latest spat between Trump and the Democrats, something that has become his norm.