Last week, House Republicans just barely passed the so-called "one big, beautiful bill" that would codify as law numerous aspects of President Donald Trump's policy agenda, and now that legislation has been sent to the Senate for its consideration.

Not all Senate Republicans are on board with the bill as written; however, Trump somewhat surprisingly encouraged the GOP senators on Sunday to "make the changes they want" to the budgetary measure, Breitbart reported.

Yet, if Senate Republicans make the "fairly significant" alterations that the president and others anticipate, those modifications risk alienating and losing the support of some House Republicans whose votes will be crucial for passage.

Senate Republicans intend to make changes to budget bill

The Washington Post reported that some Senate Republicans have problems with various aspects of the Trump agenda bill that barely passed through the House last week and are champing at the bit to make changes to an assortment of provisions that were carefully crafted to win the support of key members of Congress.

That includes possible cuts to Medicaid, the permanence of specific tax breaks, state and local tax deductions, spending cuts, and the inclusion of items that are not permitted under the rules of the reconciliation process that is being used to avoid Democratic filibusters.

Breitbart noted that a handful of Senate Republicans have also been upfront with reporters about the problem areas they see and how they are unlikely to support the current legislation unless substantial changes are made first.

Trump encourages Senate GOP to modify budget bill, if necessary

The Daily Caller reported that President Trump on Sunday talked to reporters about the status of his agenda bill in Congress and said, "I want the Senate and the senators to make the changes they want. It will go back to the House, and we’ll see if we can get them."

"In some cases, the changes may be something I’d agree with, to be honest," he continued. "We’ve had a very good response from the Senate and I don’t know how Democrats can’t vote for it. I think [Senate Republicans] are going to have changes. Some will be minor, some will be fairly significant."

As for whether the bill can be passed by both chambers and signed into law by the White House-imposed deadline of July 4, Trump remained optimistic and added, "I think it’s going to get there," as Senate Republican Leader John Thune (R-SD) and House Speaker Mike Johnson (R-LA) "have done a fantastic job" thus far.

That is somewhat different from what Trump said in a Truth Social post last week when the bill was passed, when he praised the "great job" done by Johnson and House GOP leadership to pass what he promoted as "arguably the most significant piece of Legislation that will ever be signed in the History of our Country!"

"Now, it’s time for our friends in the United States Senate to get to work, and send this Bill to my desk AS SOON AS POSSIBLE! There is no time to waste," he added at that time.

Speaker Johnson doesn't want to see lots of changes

Of course, not everyone is thrilled about the likelihood of changes being made to the budget bill that narrowly cleared the House, including Speaker Johnson, who seemed to urge his Senate colleagues to leave the legislation as-is as much as possible during an appearance on "Fox News Sunday."

"I think we reached a good equilibrium point over more than a year of discussion and negotiation and planning for our big reconciliation bill," Johnson told host Shannon Bream, per The Daily Caller. "We balanced the interests of a very diverse Republican caucus."

"We’re one team here -- House and Senate Republicans -- working together because we must. We have small margins in both chambers," the speaker added. "I encourage them to modify the package that we’re sending over there as little as possible, because we have to maintain that balance, and it’s a very delicate thing."