• President Joe Biden's fundraising operation is starting to face some new hurdles after the June debate.
• Some of Biden's campaign bundlers have paused their efforts to raise money because they are unsure if he will be the party's nominee.
• Other Biden donors have pulled back because they believe the president should drop out of the race.

President Joe Biden's fundraising operation started showing cracks in its once formidable armor, almost 10 days after his disastrous presidential debate performance.

Some of Biden's campaign bundlers have stopped making calls to potential donors since the June 27 debate, according to people familiar with the matter.

"No one is picking up the phone," said a well-connected Democratic fundraiser, who raises money for Biden and the Democratic Party. This person and others were granted anonymity in order to speak openly about private conversations on a sensitive topic.

A few of his bundlers are limiting their outreach to people in their personal fundraising networks, after they either received no response at all to asks, or else they received furious replies from people who questioned why they should give money to Biden after his substandard debate performance, according to people familiar with the matter.

Bundlers are a crucial piece of any campaign's financing strategy. Typically wealthy and well connected themselves, bundlers agree to reach out directly to people in their personal networks — both social and professional — to ask for donations for campaigns and joint fundraising committees.

Bundling is more of an art than a science. Some bundlers only ask people they know for small contributions, while others feel comfortable asking for six figure checks. The key is that a bundler spends his or her personal capital asking friends, family, clients and colleagues for what is essentially a favor — to give money to a candidate who shares their values.

Bundlers' progress is a litmus test for campaign momentum: When a candidate is on the rise, bundlers will be eager to talk to friends and family about the campaign. But if a candidate is in trouble, bundlers often feel the pullback well before it reaches campaign staffers.

Some of Biden's bundlers are weighing whether to pause their calls, texts and emails because they aren't convinced he will be in the race much longer, despite what the president says.

"I'm not going to raise any more money or write out checks until I am sure he is the candidate and the campaign finds a date" for his planned fundraiser for Biden, said longtime ally and Biden fundraiser, John Morgan.

"These next few weeks will be key. But my donors need to be sure he is the nominee," said Morgan, when asked what reassurances he wants to see that Biden will remain in the presidential race.

Other donors are stepping back because they believe the president should drop out of the race.

"It's now best for the country and the world for him to pass the baton. It's going to be a disaster for the country for him to stay in the race," said Stewart Bainum Jr., the chairman of Choice Hotels and a major Biden donor.

"We'll help the nominee — whoever that is — after the convention. We won't do it before the convention," Bainum told CNBC in an interview Monday. The nominating convention is scheduled for Aug. 19-22 in Chicago.

Bainum, who hosted a fundraiser for Biden in Maryland last year, said he believed the president would drop out of the race heading into the convention, and that the nominee would be selected by delegates.

"We want to know who the nominee is. We think there should be an open convention and the delegates can decide," he added.

Bainum and his wife Sandy Bainum have each given the legal maximum of $929,600 to the Biden Victory Fund, which benefits the campaign, the Democratic National Committee and dozens of state parties, according to Federal Election Commission records.

If Biden does not drop out, Bainum said, he fears the president will lose to former President Donald Trump, and kill any chance that Democrats have of regaining control of the House, or of holding a majority of seats in the Senate.

A Biden campaign spokesman did not return a request for comment.

As of Monday, Biden trailed Trump by 3.3 percentage points in a general election matchup, according to a RealClearPolitics polling average.

A new Bloomberg/ Morning Consult poll over the weekend showed Trump leading Biden in the key battleground states of Arizona, Georgia, Nevada and North Carolina.

In Michigan and Wisconsin, the poll had Biden up by 5 points and 3 points, respectively.

Former Pennsylvania Gov. Ed Rendell, who has continued to try to raise money for Biden since the debate, said he has heard from some donors "getting cold feet."

But Rendell also told CNBC that after the debate, he heard from Philadelphia attorney Lisa Kabnick, and she and her husband committed to giving at least $10,000 to Biden's political operation. A retired partner at Troutman Pepper, Kabnick has already given at least $25,000 to the committee, according to FEC records.

Kabnick did not reply to an email from CNBC about whether she still plans to donate to Biden.

If Biden and his political operation were to see a drop in fundraising in the coming weeks, it would be a sea change for the president, who for years has been a prodigious fundraiser for his own campaigns and for the Democratic Party.

The president's team touted $127 million raised in June, including over $30 million they said came in during the days after the debate. The overall Biden reelection effort, made up of campaign committees, allied groups and the DNC, said it started July with $240 million in cash on hand.

Still, despite Biden's efforts to reassure party donors that his debate performance was a one-off negative event, some of them are still shaken by the performance during which Biden struggled to finish sentences, maintain his train of thought, and respond with force to Trump.

The efforts to quell donor concerns appear to be having mixed results.

On Monday, Biden joined a phone call with many of his top donors, campaign manager Jen O'Malley Dillon and Maryland Gov. Wes Moore. The call started nearly 35 minutes later than the scheduled noon start time, according to a person on the call.

The president reiterated his plan to the donors on the call to stay in the race, despite deep concerns by some about his ability to defeat Trump, two people on the call said.

Biden addressed his poor debate performance by saying he planned to "attack, attack, attack, attack" Trump at the second debate in September, one of the people explained. The call lasted about a half hour.

The criticism Biden has received from party donors doesn't appear to be fazing him, even though a few, such as Disney family heiress Abigail Disney, said they are planning to halt donations to the Democratic Party until Biden drops out.

"I don't care what the millionaires have to say," Biden said in a surprise appearance on MSNBC's "Morning Joe" on Monday. "By the way, you don't see a whole lot of them flocking to Trump."

And while there is certainly worry spreading among the ranks of Democratic donors, there are still plenty willing to continue helping the president.

"I'm fully supportive of the president and plan to continue giving. He's not perfect, but the alternative is unacceptable. Not just for Democrats, but independents and many progressive traditional conservative Republicans," said Glen Tullman, CEO of Transcarent. The entrepreneur and founder of Livongo Health gave $450,000 to the Biden Victory Fund in March, according to FEC records.

There are also several fundraisers for Biden being planned across the country.

Biden is aiming to take part in a fundraiser in Austin, Texas, around July 15, the same day he is planning to deliver a speech at the LBJ Presidential Library, according to a person with direct knowledge of the matter.

He'll also be traveling to California and Colorado for a fundraising swing at the end of the month for events co-hosted by businessman Tim Gill, as well as real estate executive Wayne Jordan and his wife, longtime Democratic donor, Quinn Delaney, this person explained.

A representative for Gill did not reply to a request for comment from CNBC. Jordan did not reply to a request for comment.

Rendell said he's planning a September fundraiser for Biden in Pennsylvania. Biden's allies in New York are also planning a September fundraising event, according to a person familiar with the matter.

"Some may have been resolved not to give money, but I guarantee you that if there are polls showing him ahead of Trump, they'll start giving him money again," Rendell said.