WASHINGTON — House Republicans journeyed to the White House Thursday for a health-care victory lap in the Rose Garden, but Senate Republicans were in no mood for celebration.

Instead, they sent an unmistakable message: When it comes to health-care, we’re going to do our own thing.

“I think there will be essentially a Senate bill,” explained Sen. Roy Blunt, R-Mo., the fourth-ranking Senate Republican.

“It’s going to be a Senate bill, so, we’ll look at it,” said Sen. Jeff Flake, R-Ariz.

“We will be working to put together a package that reflects our member’s priorities with the explicit goal of getting 51 votes,” Sen. Orrin Hatch, R-Utah, reasoned.

Now that the House has narrowly passed legislation to overhaul the nation’s health care system, it is headed to the Senate, where Republican leaders will wrestle with political and procedural challenges complicating chances for final passage.

Republican senators are signaling that their strategy will be rooted in effectively crafting their own replacement for the Affordable Care Act. It remains to be seen how closely that measure will resemble the one that narrowly passed the House on Thursday.

It is also unclear whether Republican senators will resolve their differences – which on health-care have been stark.

A small group of Republican senators met Thursday morning in the office of Senate Majority Leader Mitch McConnell, R-Ky., to begin outlining their health care priorities, said Sen. John Cornyn, R-Texas, McConnell’s top deputy.

“It was designed by the leader to be a smaller group of people that represent the different perspectives and points of view in our conference,” Cornyn said. “If that group can get to yes, then (we will) take it to the rest of the conference.”

But Cornyn would not commit to a timeline for a Senate vote, simply saying: “When we get 51 senators, we’ll vote.”

Republicans hold a 52 to 48 advantage over Democrats in the upper chamber, leaving Republican leaders with a narrower margin for error than in the House – where infighting among Republican lawmakers nearly derailed the push on multiple occasions.

In a sign of the frustration that some Republican senators already have with the House bill, Sen. Lindsey Graham, R-S.C., posted a skeptical note on Twitter Thursday: “A bill – finalized yesterday, has not been scored, amendments not allowed, and 3 hours final debate – should be viewed with caution.”

Senate Republicans have opted to use a maneuver known as reconciliation to try to pass the bill with a simple majority, instead of having to clear the 60-vote threshold that is required for most legislation. In the current balance of power, that would require Democratic votes. But even getting to a simple majority will be no small task.

Republican senators from states that have expanded Medicaid under the Affordable Care Act, such as Sen. Rob Portman of Ohio and Shelley Moore Capito of West Virginia, have voiced concerns about rollbacks to that program in the House bill.

“Absolutely,” replied Capito, when asked if she has still has worries.

Meanwhile, three conservative senators – Ted Cruz, R-Texas, Mike Lee, R-Utah, and Rand Paul, R-Ky., – are also wild cards. They have been willing to buck party leadership; earlier this year, they pushed for a more aggressive repeal of the health-care law than many of their colleagues favored.

“I think that the House Freedom Caucus was able to make the bill a lot less bad,” said Paul. “I think there’s still some fundamental problems that I have with it.”

Sens. Bill Cassidy, R-La., and Susan Collins, R-Maine, have already introduced an alternative plan, giving lawmakers a second measure to look at should talks fall apart over the current bill.

Senate Republicans will also need to clear procedural hoops, which could steer them to strip away some of the House bill’s signature provisions.

The measure’s original version, introduced in March by Speaker Paul D. Ryan, R-Wis., contained elements at risk of being struck out in the Senate under budget reconciliation rules that allow tax and spending changes but not broader policy changes.

That proposal initially left many of the ACA’s insurance regulations alone – with the goal of ensuring it would pass muster with the Senate parliamentarian, a nonpartisan officer of the Senate who decides what may go in a reconciliation bill – but not all of them.

The version of the bill the House passed Thursday undercuts the ACA’s insurance regulations even more, by giving states a path to opt out of federal requirements for insurers to cover certain “essential” health benefits – and to allow them to charge sick people the same premiums as healthy people.

The Republican bill would allow insurers to charge older Americans five times what they charge younger people, as opposed to three times as much under current law. And it would enable insurers to hike premiums by 30 percent for people who don’t remain continuously covered. Health policy experts, including conservative ones, have noted that the parliamentarian may decide those provisions need to be stripped out.

Also, members of the House voted on their bill before they received a score from the nonpartisan Congressional Budget Office, which measures how much the legislation would cost and how many people stand to lose coverage under it. Senate budget rules require a CBO score that proves the legislation will not increase the deficit after 10 years. The Senate parliamentarian can’t even start reviewing the bill without a score from the CBO, which is expected to take several weeks.

“I sincerely hope the Senate won’t mimic the House and try to rush it through without hearings or debate or analysis,” said Senate Minority Leader Charles Schumer, D-N.Y.

The CBO projected in late March that an earlier version of the health-care plan would result in 14 million more people being uninsured in 2018 than under current law. It projected the plan would slash the federal deficit by $150 billion between 2017 and 2026.

Even if Senate Republicans manage to pass their own version of a health-care overhaul, it will then have to be reconciled with the House version. And if getting House conservatives and moderates to pass their initial measure was a challenge, it could be next to impossible to get enough of them to sign on to whatever the Senate decides to pass.

Rep. Mark Meadows, R-N.C., chairman of the hard-right House Freedom Caucus that Paul referenced, said he will not necessarily back any changes made by the Senate.

“Obviously, the upper chamber has their own personalities and their own agendas,” Meadows said. “Certainly, it’s their agenda and not mine.”

“If they revise it, there’s no way,” Rep. Dave Brat, R-Va., another Freedom Caucus member, said earlier this week. Brat refused to support the Ryan bill until provisions were added for states to opt out of more insurance regulations.

“Have you been watching for the last few months how tight this is, and you’re going to shift this one or the other?” Brat said. “Good luck, you don’t have to be Einstein to game theory that one.”