A balanced-budget amendment that Senate Republicans had planned to roll out this week is now on hold until after Congress’s upcoming week-long recess.

The proposal was to be unveiled by five Senate Republicans on Thursday, but they agreed in a Wednesday meeting with Minority Leader Mitch McConnell (R-Ky.) to postpone the public unveiling of the legislation until all Senate Republicans had signed onto it, according to a source with knowledge of the meeting.

Asked Thursday about the delay, Sen. Mike Lee (R-Utah), one of the co-authors of the amendment, said that the issue was mostly one of timing and expressed confidence that the entire Republican conference would eventually sign on.

“I do believe we’ll be able to get all of the Republicans on board. . . . There are a lot of things happening right now; I think there were some people who probably sensed that we could find a better moment to release it. But it is not a substantive disagreement as to the need for a balanced-budget amendment; it was an issue mostly related to timing,” Lee said.

Along with Lee, the other Republicans spearheading the balanced-budget effort are Sens. Orrin Hatch (Utah), Jon Kyl (Ariz.), John Cornyn (Texas) and Pat Toomey (Pa.).

The balanced-budget amendment merges two separate plans proposed earlier this year, one by Lee and another by Hatch. As of Friday, 38 of the 47 Senate Republicans had signed onto at least one of the two proposals.

The nine who have not are McConnell and Sens. Lamar Alexander (Tenn.), Scott Brown (Mass.), Dan Coats (Ind.), Bob Corker (Tenn.), Ron Johnson (Wis.), Jeff Sessions (Ala.), Richard Shelby (Ala.) and David Vitter (La.).

Earlier this month, the Republican caucus united in favor of a measure, sponsored by Lee, that would have “expressed the sense of the Senate” in support of a balanced-budget amendment. That suggests that gathering their support for the combined Lee-Hatch plan is indeed within reach.

Getting the measure passed is a far greater hurdle, however: The amendment requires the approval of a two-thirds majority in both chambers and ratification by three-quarters of the states.

The last big balanced-budget effort in the Senate, led by Hatch in 1997, won the backing of 66 senators, one short of passage.

The “sense of the Senate” vote earlier this month did not bode well for the current Republican-led effort. Fifty-eight senators — including 11 members of the Democratic caucus — expressed their support for a balanced-budget amendment, meaning that nine more Democrats would need to sign on in order for the amendment to pass.

The combined Hatch-Lee measure would require a balanced budget for each fiscal year and would mandate that any tax increase receive a two-thirds-majority in both chambers to pass.

It also would require a two-thirds roll call vote in both chambers before the government could run a deficit in a particular year. Any effort to raise the debt ceiling would need to be approved by a three-fifths vote in both chambers.

And it would cap spending at no more than 18 percent of gross domestic product. Currently, federal spending amounts to 25 percent of GDP.

The amendment would go into effect in the fifth fiscal year after ratification — a longer timeline than either Lee or Hatch originally proposed. And it contains a provision allowing for the balanced-budget and spending-cap requirements to be waived when the country is at war or engaged in military conflict that poses an “imminent and serious” threat to national security.

In the House, a separate proposal for a balanced-budget amendment has garnered more than 200 co-sponsors, including a handful of moderate Democrats.