Senate Republicans are signaling they are in no hurry to move legislation to repeal and replace ObamaCare after it passed the House Thursday.

“There is no timeline,” Sen. John Cornyn John CornynSenate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll Republican Senators raise concerns over Oracle-TikTok deal MORE (Texas), the Senate’s No. 2 Republican, said when he was asked about a schedule for when the Senate could move a bill.

Asked if action during the current work period running through the end of the month was “realistic,” he added: “There is no timeline. When we get 51 senators, we’ll vote.”

The House narrowly passed legislation, the American Health Care Act, in a 217-213 vote, fulfilling a years-long pledge and sending the bill to the Senate.

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Sen. Roy Blunt Roy Dean BluntOn The Money: Trump undercuts GOP, calls for bigger COVID-19 relief package | Communities of color hit hardest financially by COVID-19 | Businesses, states pass on Trump payroll tax deferral Trump undercuts GOP, calls for bigger COVID-19 relief package Businesses, states pass on Trump payroll tax deferral MORE (R-Mo.), a member of GOP leadership, also signaled that Republicans are focused on getting a deal that can pass rather than sticking to a specific timeline.

“I can’t imagine there will be a rush to take up the bill as much as a real concentrated effort to find where the 51 votes might be if the 51 votes are still available,” he told reporters.

The House GOP bill is expected to have to undergo significant changes in the upper chamber to meet budgetary rules that would allow it to block a Democratic filibuster.

Sen. Chuck Grassley Charles (Chuck) Ernest GrassleySenate Republicans signal openness to working with Biden Senators offer disaster tax relief bill Trump spikes political football with return of Big Ten season MORE (R-Iowa), the chairman of the Judiciary Committee, said he had been asked if lawmakers would be able to pass a bill by June 19 — a key date for insurance companies — but couldn't commit to the timeline.

“I said there’s no assurance I can give you from a substance standpoint or a process standpoint for when that’s going to happen because there’s been such little discussion,” he said.

McConnell has convened a working group of senators as they look for legislation that could pass the upper chamber. Cornyn noted the group met for a second time on Thursday. Lawmakers could also need to go a conference with the House to work out their differences, which would drag out the process.

The hedging on a timeline for the Senate comes after Sen. Lindsey Graham Lindsey Olin GrahamSenate Republicans signal openness to working with Biden Loeffler calls for hearing in wake of Netflix's 'Cuties' Quinnipiac poll shows Graham, Harrison tied in South Carolina Senate race MORE (R-S.C.) raised concerns about the rapid pace the House took to pass the legislation. The House voted on the bill even though it did not have a Congressional Budget Office (CBO) score.

A bill -- finalized yesterday, has not been scored, amendments not allowed, and 3 hours final debate -- should be viewed with caution. — Lindsey Graham (@LindseyGrahamSC) May 4, 2017

Several moderate GOP senators came out against an initial version of the House bill that was pulled from the floor in March, over concerns about what happens in their states to ObamaCare’s expansion of Medicaid, the federal low-income healthcare program.

Sen. Susan Collins Susan Margaret CollinsThe Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally Gideon leads Collins by 12 points in Maine Senate race: poll Senate leaders quash talk of rank-and-file COVID-19 deal MORE (R-Maine) urged her colleagues to not move health legislation quickly.

“I think we should take as long as necessary to do the job right, and we certainly need the CBO analysis on the impact of cost and coverage...before we can produce our own bill,” she told reporters.

GOP Sen. Dean Heller Dean Arthur HellerOn The Trail: Democrats plan to hammer Trump on Social Security, Medicare Lobbying World Democrats spend big to put Senate in play MORE (Nev.), the Senate’s most vulnerable Republican up for reelection, and Rob Portman Robert (Rob) Jones PortmanRomney undecided on authorizing subpoenas for GOP Obama-era probes Congress needs to prioritize government digital service delivery House passes B bill to boost Postal Service MORE (Ohio) reiterated after the Thursday vote that they could not support the House bill in its current form.