(CNN)Bipartisan Senate leaders have agreed to limit debate on a long-sought budget deal — setting up a vote on the package, though as of Wednesday morning it’s not clear when they would vote.

Senators are trying to clear other key items off the chamber’s to-do list before senators leave for a five-week Senate recess, putting Republican rank-and-file up against a wall where some will have to decide whether to back the President’s $2.7 trillion budget deal or face the ire of a President who hasn’t taken kindly in the past to defectors.Exact timing of the vote on the budget deal is not locked in yet but is expected to be announced by Senate Majority Leader Mitch McConnell sometime Wednesday — meaning the vote could come in the afternoon or evening or slip to Thursday.When asked about vote timing Wednesday, McConnell did not respond.”It’s going to pass,” the Kentucky Republican told reporters. Read MoreGOP leaders are not giving passes for “no” votes and the goal is still to convince half or more of the conference to vote for the budget deal. Leaders want to avoid a show like the one in the House where there was a massive Republican uprising against the package negotiated by Treasury Secretary Steven Mnuchin and blessed by the President. Again, this bill is expected to pass (mostly with Democratic votes), but leaders want to stave off any surprises and want to make sure the President knows that his party is behind a top priority to raise the debt ceiling and stop automatic spending cuts on the defense budget.And it’s not just congressional leaders. A GOP source close to the process told CNN that the President Donald Trump, Vice President Mike Pence and Secretary of Defense Mark Esper have made a small handful of calls to GOP senators to talk about the budget deal.Esper especially has focused his calls on trying to explain to members that $738 billion and $740 billion in defense spending in year one and two might respectively fall a tad bit short of the Department of Defense’s hope for $750 billion in their strategic planning memo, but that the certainty that the money is coming makes up for the small shortfall. That has been a concern for some Republicans.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.”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. On Tuesday, senators began a long series of nighttime procedural votes on judges and executive branch nominees, including 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. This story has been updated with additional developments Wednesday.

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