Republican Sen. Lisa Murkowski released a lengthy new statement on her vote in support of President Trump's domestic policy bill, which narrowly passed the Senate earlier Tuesday.

Calling it "one of the hardest votes" she has taken during her time in the Senate, the Alaska lawmaker explained her thinking behind voting for the bill in the end, despite her many concerns over cuts to Medicaid and food stamps. She noted it is the "people of Alaska that I worry about the most."

“But, let’s not kid ourselves," she continued. "This has been an awful process -- a frantic rush to meet an artificial deadline that has tested every limit of this institution. While we have worked to improve the present bill for Alaska, it is not good enough for the rest of our nation -- and we all know it."

“My sincere hope is that this is not the final product. This bill needs more work across chambers and is not ready for the President’s desk. We need to work together to get this right.”

The House Rules Committee convened on Tuesday afternoon to markup the Senate version of Trump's sweeping domestic policy bill. The markup is expected to last for hours.

"H.R.1 has returned to the people's House with final consideration," Rules Committee Chair Virginia Foxx said as she kicked off the markup. "And while I don't often think that the other body improves our legislation, it's important to recognize that much of what the House included in H.R.1 when we initially passed, it is still included."

"A failure to pass this legislation, carries with it, serious negative implications, not only for hardworking taxpayers, but also the nation," Foxx added.

Rules Committee ranking member Jim McGovern, a Democrat, said if the "ugly bill" passes in the House, "it's going to get a lot uglier when people realize what's in it, and not even Donald Trump's new $300 bottle of cologne will cover the stench."

"We are here today on a bill that just dropped from the Senate hot off the press, passed only an hour ago," McGovern said. "It's massive here. It is nearly 1,000 pages long, and I've got to ask: Have any of you read it this time? Because last time we met on this legislation, many of our Republican colleagues had not."

-ABC News' Lauren Peller

Senate Majority Leader John Thune, celebrating after steering the approval of President Trump’s megabill, nodded to all of the “work” that went into its passage.

“This doesn't happen easily, for sure, and in this case, it took a lot of time and probably a lot less sleep than I think most people were hoping for. But in the end, we got the job done, and we're delighted to be able to be partners with President Trump and his agenda, an agenda that is the right one for the American people, the one that they voted for last November," he told reporters at the Capitol.

Thune also acknowledged the difficulty House Republicans might have in passing the package as it now heads their way, but said he delivered them a “strong product.”

“Well, we'll see. I mean, you know how hard it was to pass it -- I think the House, I appreciate the narrow margins they have over there … but I think we gave a really strong product,” he said.

“I think we took what they sent us and strengthened and improved upon it. And so I'm hopeful that now, when it gets sent over there, as they deliberate about how they want to handle it, they'll find the goals that are necessary to pass it,” Thune added.

-ABC News' Isabella Murray

Speaker Mike Johnson and top Republican leaders announced in a statement that the House will consider the bill "immediately for final passage" -- with renewed intent to put the measure on President Trump's desk by July 4.

"The House will work quickly to pass the One Big Beautiful Bill that enacts President Trump's full America First agenda by the Fourth of July. The American people gave us a clear mandate, and after four years of Democrat failure, we intend to deliver without delay," the leaders said.

“This bill is President Trump’s agenda, and we are making it law. House Republicans are ready to finish the job," they added.

The House Rules Committee will convene at 1:30 p.m. ET on Tuesday to markup the bill and set parameters for floor debate and consideration of the bill.

-ABC News' Lauren Peller