Top Senate Republicans and members of the Trump administration will sit down Tuesday as they turn their attention to how to avoid a government shutdown starting on Oct. 1.

Senate Appropriations Committee Chairman Richard Shelby Richard Craig ShelbySenate to push funding bill vote up against shutdown deadline Senate GOP eyes early exit Dems discussing government funding bill into February MORE (R-Ala.) and Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump 'no longer angry' at Romney because of Supreme Court stance On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline The Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power MORE (R-Ky.) will meet in the Capitol with acting chief of staff Mick Mulvaney Mick MulvaneyOn The Money: House panel pulls Powell into partisan battles | New York considers hiking taxes on the rich | Treasury: Trump's payroll tax deferral won't hurt Social Security Blockchain trade group names Mick Mulvaney to board Mick Mulvaney to start hedge fund MORE, Treasury Secretary Steven Mnuchin Steven Terner MnuchinOn The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline Vulnerable Democrats tell Pelosi COVID-19 compromise 'essential' Pelosi asks panels to draft new COVID-19 relief measure MORE and Office of Management and Budget Director Russell Vought.

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Shelby said the "goal" of the talks was to get a deal to allow the Appropriations Committee to start moving government funding bills. Lawmakers have to pass 12 appropriations bills, either individually or as part of a package, if they want to avoid a shutdown. So far the committee has passed none.

"The goal would be is that here it is, it's June, early June … and it's time to start marking up some bills. The question is can we mark it up to certainty or uncertainty, and we're looking to start the process," Shelby said.

Part of the wrinkle for the Senate in starting to move appropriations bills is that they don't yet have a deal to lift defense and nondefense spending caps. Without an agreement, steep, across-the-board cuts, known as sequestration, are set to kick back in. Lawmakers use the agreement to determine the totals of the 12 appropriations bills.

Shelby acknowledged that Senate Republicans could follow the path of House Democrats and "deem" working spending levels, even if they have to be reconciled with the budget caps figures later this year, to at least get the process moving. Senate appropriators had previously pointed to the third week of June as when they wanted to start moving government funding bills in the committee.

"We can assume or 'deem' a number. We want it to be a realistic number and we want the administration to know what we're doing because we work with them," Shelby added.

The decision to potentially start moving appropriations bills comes after talks about a deal to lift the defense and nondefense budget caps appeared to stall after a meeting with top congressional leaders and Mulvaney, Mnuchin and Vought last month.

McConnell had initially indicated he thought a deal could come together quickly, but Schumer acknowledged that they were still far apart on the top line number for nondefense spending, a major priority for Democrats.

"I still believe that a spending caps deal is to everybody's advantage. Everybody. The president, the Senate, the House, both parties. We expect those talks to resume and we're hopeful we'll be able to reach an agreement so we can have some kind of ordinary process that could fund the government of the United States. So, I remain optimistic," McConnell told reporters last week.