The top four congressional leaders of both parties are expected to meet with White House officials next week to discuss a two-year budget deal, a pair of sources confirmed Friday.

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The meeting comes after Mulvaney met with McConnell on Thursday to discuss spending and amid growing concerns on Capitol Hill about avoiding across-the-board cuts known as sequestration.

"What could come out of it is an agreement, where we can move our approps, a number," Shelby told The Hill when asked what could come out of the White House talks. "Or nothing could come out if, you've been here, you've seen."

A senior White House official told The Hill that "it’s still too early to speculate on what the outcome of these discussions will be, but as deficit spending continues to drive up our national debt, the Administration will continue to push for fiscal responsibility."

Lawmakers have been sounding the alarm about the need to keep the government open, with current funding set to expire at the end of September. They'll also need to raise the debt ceiling later this year to avoid defaulting, with the Treasury Department expected to be able to extend the deadline until September or October.

Unless lawmakers reach a deal on spending, about $120 billion in automatic cuts to defense and domestic programs would go into effect under sequestration.

Separately, Pelosi and Schumer plan to meet with Trump next Wednesday to follow up on their recent meeting about a $2 trillion infrastructure plan.

—Updated at 4:26 p.m. Brett Samuels contributed.