Senate Republicans won't delay their leadership elections set for next week despite a growing number of calls from conservative senators who want a postponement and are growing frustrated with Minority Leader Mitch McConnell and other leaders.

"It makes no sense for Senate to have leadership elections before GA runoff," Sen. Ted Cruz, R-Texas, tweeted Friday. "We don’t yet know whether we’ll have a majority & Herschel Walker deserves a say in our leadership. Critically, we need to hear a specific plan for the next 2 yrs from any candidate for leadership."

Sen. Marco Rubio, R-Fla., also tweeted Friday that the leadership vote "should be postponed." Sen. Cynthia Lummis, R-Wyo., tweeted in support of Rubio's proposition. So did Sen. Josh Hawley, R-Mo., who has vocally opposed bringing McConnell back as the top Senate Republican.

But a Senate GOP aide confirmed to Fox News Digital that elections will go on as planned.

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Former President Donald Trump has repeatedly called for McConnell, R-Ky., to be replaced as party leader.

McConnell has been in uncomfortable positions within his party in recent years. He was in the minority of his party in voting for several pieces of legislation in the current Congress, including an infrastructure bill, a China competition bill and a gun control bill.

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Those votes are among the reasons multiple GOP Senate candidates said they would not vote for McConnell to have another term as leader, including Senator-elect Eric Schmitt, R-Mo.

Sen. Rick Scott, R-Fla., has also repeatedly refused to say he'll support McConnell for party leader or rule out challenging him for the role.

But McConnell still has a lot of cushion before his bid to become the longest-serving party leader in Senate history is at risk. Unlike House speaker elections, which require a majority of the chamber, senators elect their party leaders by a simple majority of the conference.

It's not expected that enough members will come out in opposition to McConnell to oust him from his leadership post, and comments today made it appear unlikely that leadership elections would be postponed.

"Members are frustrated, and they’re looking for an outlet to have a conversation. There will be a robust discussion at lunch on Tuesday," at Senate GOP aide told Fox News Digital. "There will also be a lot of questions about candidate quality/campaign priorities and mistakes. A lot of these will be directed at Scott, especially if the reports are true that he was preparing to challenge McConnell before Election Day had even concluded."

Fox News' Chris Pandolfo contributed to this report.