Washington (CNN) Senate Republican leaders are facing mounting pressure from President Donald Trump and a vocal group of rank-and-file senators to pass a series of spending bills ahead of their summer break and avoid a year-end messy fight to keep the government open, like the ones that have plagued Congress in the past.

Trump tweeted over the weekend that he wants Congress to pass its annual spending legislation before the typical August recess -- or, as he wrote, "NOT GO HOME."

"I agree with him," said Republican Sen. John Kennedy of Louisiana. "I'm embarrassed that we don't follow the law."

Kennedy was one of 16 Republican senators who signed a letter to Senate Majority Leader Mitch McConnell, urging the Kentucky Republican to cancel the summer recess so they can get more work done.

"We stand ready to work Mondays and Fridays, nights as well as weekends, to ensure the funding process is not used to jam the President with a bad spending deal," the senators said.

McConnell, according to one person briefed on the matter, is seriously considering scrapping some or all of the August recess, something he did a year ago to help confirm a backlog of nominations and other legislative business.

Politically, this person notes, such a move could help the GOP since there are many more Democratic incumbents in tough races up for re-election, and this would effectively keep them in Washington ahead of the midterms.

What's the rush?

Congress is up against an October 1 deadline, the start of the next fiscal year, to pass 12 appropriations bills, each funding vital parts of government, such as defense, homeland security and agriculture.

Congress faces this deadline every year but routinely misses it, relying on shorter term spending bills, known as continuing resolutions, to sustain Washington instead. Last year, Congress blew past the fall deadline and used five continuing resolutions to get by until it approved a massive, $1.3 trillion spending bill all at once in March -- more than 150 days after the deadline.

That pattern has become par for the course on Capitol Hill. According to the Pew Research Center , Congress hasn't passed all 12 spending bills on time since 1997.

And Trump isn't happy about that. When Congress passed that massive spending bill late in March -- all in a big package known as an omnibus -- Trump said he would never sign another bill like that.

"To prevent the omnibus situation from ever happening again, I'm calling on Congress to give me a line item veto for all government spending bills and the Senate must end -- they must end -- the filibuster rule and get down to work," he said in March.

He's referring to complicated Senate procedures that gum up and delay the process. The House typically churns out its appropriations bills at a reasonable rate -- since those bills require only a majority vote in the House -- but the Senate requires a stricter threshold of 60 votes out of 100, meaning they must have some bipartisan approval.

How are they trying to make it work this time?

Leaders in both parties say they truly want to return to a time of consistently passing carefully crafted and vetted spending bills that reflect updated needs and priorities for the government. A group of bipartisan Senate leaders recently reached a handshake agreement to try to move the 12 annual appropriations bills efficiently.

"I'm somewhat optimistic based on the conversations I've had with the Democratic leader," McConnell told reporters Tuesday. "that we're going to have a higher level of cooperation than we've had, and we'll see how that works out."

The Senate minority leader, New York Democrat Chuck Schumer, agreed, saying he didn't think senators would need to work through August to pass the bills.

"I think we're going to have plenty of time to get done what we need to be done if everyone cooperates," he said a few minutes after McConnell spoke.

But taking the practical steps to make that happen could be harder than it seems, even with a newfound spirit of cooperation. Any single senator -- from either party -- unhappy about anything can cause long and unexpected floor delays. If McConnell, for instance, scrapped the August break, it could inflame tensions and hamper cooperation on appropriations.

And with just 14 legislative weeks before the end of the fiscal year, aides in each party acknowledge it may not be possible to pass all 12 bills. Trump's request for a border wall is one potential roadblock for the bill to fund homeland security, for example. Democrats strongly oppose building a wall, and talks could collapse if Trump insists on wall funding.

Sen. Richard Shelby, a Republican from Alabama who chairs the Appropriations Committee, said he thinks they can get four or five bills done by the deadline.

"It's tough but doable," he told CNN.

Georgia's Republican Sen. David Perdue, who spearheaded the letter to McConnell urging him to work longer weeks and cancel the August recess if necessary, suggested McConnell consolidate the 12 bills into a few smaller packages to help expedite passage.

In addition, McConnell has made confirming Trump's slate of conservative judges a top priority -- a decision that has dominated floor action for months. McConnell would have to set aside precious floor time from that effort to take up spending bills for federal agencies.