By Ted Barrett and Lauren Fox, CNN

Bipartisan Senate leaders agreed Tuesday to limit debate on a long-sought budget deal -- setting up a vote on the package Wednesday, according to Democrats -- and clear other key items off the chamber's to-do list before senators leave for a five-week Senate recess.

Senators began a long series of nighttime procedural votes on judges and executive branch nominees including President Donald Trump's choice for UN ambassador, Kelly Craft. Final confirmation votes for many of the judges are expected Wednesday. Democrats said Republicans would not reach their goal of confirming 19 district court judges before the recess, and those remaining judges would have to wait until September to be confirmed.

Meanwhile, Senate Republican leaders continued their aggressive whip the vote count on the spending caps and debt limit agreement, with an eye towards ensuring in passes with the support of at least half the GOP conference, unlike when it passed out of the House last week with most Republicans voting against it.

"We are in the process of working that vote," Sen. John Thune, the second-ranking GOP leader and whip, when asked by CNN if he expects a majority of Senate Republicans to vote for the bill. "I'm hopeful and optimistic that when the time comes, we'll have the votes to get it done."

Senate Majority Leader Mitch McConnell is working to convince rank-and-file members to back the bill because it has a big increase in defense spending, a top GOP priority, and because Trump backs it.

"Given the realities of divided government, it is a strong deal that achieves my Republican colleagues' and my No. 1 priority: Continuing to invest seriously in rebuilding the readiness of our Armed Forces and modernizing them to meet the challenges of today," McConnell said. "The Trump administration has negotiated their way to a major win on defense. The House has passed the compromise legislation. The President is ready and waiting to sign it."

But many conservative Republicans worry the package is just too expensive.

"At the end of the day, there's tremendous amounts of new spending, way over and above what we need to secure our national defense," said freshman Sen. Josh Hawley, a Republican from Missouri. "I think it's irresponsible and not for any clear purpose beyond the defense portion, which I support."

The job of wrangling "yes" votes got harder for GOP leaders when Sen. John Kennedy, a Republican from Louisiana, who was leaning against the bill, announced publicly he would vote "no."

"It does add additional money for defense," Kennedy said. "But I view if from a different perspective. I think we could have done a much better job, or at least tried harder, to save money."

Kennedy predicted the bill will pass but couldn't say if more than half his GOP colleagues would support it.

"Yeah, I just don't know with how many Republican votes," he said. "I think you'll see more than just a handful vote against it for the reasons I just articulated."

Sen. Cory Gardner, a Republican from Colorado up for reelection, said he is concerned "it's just a lot of money and at some point, things become so free, we can't afford it."

One GOP senator on the fence acknowledged that some of his colleagues would like to vote against it to publicly demonstrate they are fiscally prudent while privately hoping it passes so there can be orderly governing out of Washington.

"There are a lot of people who will vote 'no' who hope to heck it passes," said the senator who did not want to be identified.

Exact timing of the vote on the budget deal is not locked in yet but is expected to be announced by McConnell sometime Wednesday.