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When the Republican presidential hopefuls take the stage in Milwaukee on Tuesday night for their fourth debate, familiar faces will be missing from the prime-time lineup — Mike Huckabee and Gov. Chris Christie of New Jersey.

On Thursday, Fox Business Network, the host of the debate, announced on “Lou Dobbs Tonight” the qualifiers for the main stage, and Mr. Christie and Mr. Huckabee — who had been slipping in recent polls — did not quite make the cut.

Then lineup for the main stage debate will be Donald J. Trump, Ben Carson, Senator Marco Rubio of Florida, Senator Ted Cruz of Texas, Jeb Bush, Carly Fiorina, Gov. John R. Kasich of Ohio and Senator Rand Paul of Kentucky.

To qualify for the prime-time debate based on the network’s criteria, candidates needed to score at least 2.5 percent or higher in an average of the four most recent national polls through Nov. 4. Those below the 2.5 percent average in the polls could qualify for the so-called undercard debate, as long as they hit at least 1 percent in at least one of the four most recent national polls.

Dropping off the main stage is a huge blow to Mr. Christie, who has struggled to gain the traction for which he’d hoped ever since announcing his bid, and who saw his “tell it like it is” message inadvertently usurped by Mr. Trump’s freewheeling, tell-it-like-it-is campaign.

Mr. Christie seemed prepared for the news, tweeting within seconds of the announcement that “it doesn’t matter the stage, give me a podium and I’ll be there to talk about real issues like this,” with a link to his now-viral video speaking about drug addiction.

An hour or so later, Mr. Huckabee shared a similar sentiment.

“I’m happy to debate anyone, anywhere, anytime,” he said in a statement, adding, “Washington is stealing from seniors, punching American workers in the gut, and bankrupting our kids and grandkids. I refuse to let that stand.”

For Mr. Huckabee, it’s another example of his struggling to find a path in the crowded Republican field. He has been unable to gain the traction among evangelicals that helped fuel his rise in 2008 as Mr. Cruz and Mr. Carson resonate strongest with that bloc.

The debates, which so far have shattered ratings records, have been critical in helping candidates gain national attention and boost themselves in the eyes of donors and voters — and falling from the main stage to the undercard is likely to hurt Mr. Christie with donors and national exposure.

Mrs. Fiorina, the former chief executive of Hewlett-Packard, used her strong performance on the undercard stage in the first debate, hosted by Fox News, to launch herself into the upper tier of candidates, and she subsequently rose in polls after her strong performance at her prime-time debate debut on Sept. 16.

The candidates who have been relegated to the “junior varsity” debate have struggled to capture voter and media attention. That lineup will include Mr. Christie, Mr. Huckabee, Gov. Bobby Jindal of Louisiana and Rick Santorum.

Senator Lindsey Graham of South Carolina, who has had some strong performances in the earlier debates, was unable to gain much traction nationally, so much so that he and George E. Pataki will be left off of the undercard debate stage all together. They both failed to meet the 1 percent minimum requirements set by Fox Business News.

Mr. Graham’s campaign released a statement after the announcement expressing disappointment in the network’s choice of polling.

“Regardless of this decision tonight, Senator Graham continues to be the foremost expert on foreign policy and national security in this field of candidates, on either stage,” Christian Ferry, the campaign manager, said. He added, “In the end, the biggest loser tonight is the American people and the Republican presidential primary process that has been hijacked by news outlets.”

Mr. Pataki was similarly displeased.

“Running for the most important leadership position in the world shouldn’t be reduced to the level of ‘American Idol’ or ‘Survivor,’ ” Mr. Pataki said in a statement.

Mr. Graham and Mr. Jindal are both pushing the networks to hold two 90-minute prime-time debates with seven candidates — chosen randomly — on each stage.

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