Washington (CNN) Joe Biden has long wanted nothing more than this: a head-to-head matchup with President Donald Trump to show Democrats that he is the party's best chance of winning the White House.

But as his extraordinary battle with Trump enters its third week -- and the impeachment inquiry intensifies -- Biden is struggling to prove that point as he searches for the proper footing to fight the President without being sullied by the fallout. He's under siege by Trump and the explosive Ukraine investigation even as he tries to regain command of the Democratic primary race.

"I'm not going anywhere," Biden told donors this past weekend during a closed-door retreat in Philadelphia, a person in attendance told CNN -- a message he also delivered in a speech late last week and in a Washington Post op-ed aimed squarely at Trump. "You won't destroy me and you won't destroy my family."

At this critical juncture for Biden's candidacy, the official position inside the campaign is that this noisy feud with Trump elevates the former vice president's standing in the Democratic race.

Yet even his most loyal supporters and longtime advisers concede they can't be certain whether that's true, given the uncertainty surrounding the politics of impeachment and his fragile position in the primary fight.

"I'm not going to sit here and say there is no concern," a Biden confidant told CNN, speaking on condition of anonymity to discuss internal campaign conversations. "As this drags on, we just don't know. No one knows."

Challenges ahead

For all of the planning and deliberations that went into his presidential bid, more than a dozen aides, donors and top supporters to Biden acknowledged in weekend interviews the campaign was entering almost entirely uncharted terrain as it grappled with the confluence of three distinct challenges.

First, the threat Elizabeth Warren's candidacy presents to Biden is more serious than ever. Not only did she announce Friday that she had outraised him by nearly $10 million over the last three months, she also has the ability to return to those grassroots donors again and again as she works to consolidate the party's progressive wing. Biden has been far more reliant on traditional fundraising, which places him at a distinct disadvantage among his leading primary rivals.

Second, the utter unpredictability of Trump and his attempts to draw Biden into the fray presents an unwieldy challenge. Biden does not want to get pulled into "a mud fight," as he told donors last week in California, yet early attempts to respond to the President's bombastic claims left many senior Democrats saying Biden looked weak and imploring the campaign to ramp up its response.

Third, the injection of Hunter Biden into the fray complicates an already fraught private family dynamic. Despite unfounded allegations that the former vice president intervened to help his son in Ukraine and China, the campaign has struggled to respond to almost daily taunts from Trump and his followers.

Fighting a war on these three distinct fronts has awakened anxieties inside the Biden campaign and among his supporters. While Warren's ascendancy may typically spark the most worry in a typical campaign season, aides say she is almost relegated to the back burner, which could create challenges of its own.

"None of this is going away," said a senior Democrat official who admires Biden, but is troubled by the campaign's response to Trump. "He needs to show more emotion and find a way to turn all of this into an advantage."

Over the weekend in Philadelphia, dozens of Biden donors gathered for a tour of campaign headquarters and to receive an update on the state of the race from top Biden advisers, including campaign manager Greg Schultz and longtime adviser Steve Ricchetti. The event was scheduled long before the impeachment inquiry began, aides said, but, in the context of the drama unfolding in Washington, it took on a heightened sense of urgency.

After initially taking a far more measured approach to the crisis, Biden and his campaign have stepped up their attacks on Trump on multiple fronts in recent days, from paid advertising to fundraising appeals to more aggressive responses. The shift in strategy comes after the campaign received a fusillade of advice from Democrats watching in frustration.

"This campaign will continue to focus on the issues that impact people's lives," deputy campaign manager Kate Bedingfield wrote in a weekend memo, "while simultaneously hammering Donald Trump for his unprecedented abuse of power and correcting the record on the mountain of lies Trump and his allies continue to spread about Joe Biden."

Striking a proper balance between offensive and defensive moves -- juggling primary opponents and a potential general election rival -- has proven remarkably tricky. The challenges from Trump come just as more voters are tuning into the 2020 campaign and as Biden loses his frontrunner's advantage in on the race.

Democratic Sen. Bob Casey of Pennsylvania said he had little doubt Trump was trying to weaken Biden's candidacy because Republicans would prefer to run against Warren or another candidate with positions far more liberal than Biden. He said Democratic voters should not allow Trump to hijack their primary campaign.

"The American people know Joe Biden and his character and values," Casey said in an interview. "We should not allow Trump to change the subject and distract from a clear abuse of power."

Warren was already a rising threat, but raising $24.6 million -- compared to Biden's $15.2 million -- sent alarm bells throughout the campaign and among top donors. Several Biden campaign officials used the fundraising comparisons, along with Bernie Sanders' $25 million haul, as a plea for donors to step up their efforts.

"Sanders and Warren have been building an online fundraising mechanism for six years. Joe Biden's been building one for six months," said Dick Harpootlian, a South Carolina Democratic state senator who has hosted a fundraiser for Biden. "We've got to raise some money. His online efforts are getting better, but he's going to continue to have to do fundraisers which takes away from his time to campaign."

On the policy front, advisers to Biden say they will gradually sharpen differences, particularly on Warren's support for the single-payer "Medicare for All" proposal. But they have no plans to use a scorched-earth campaign against the Massachusetts senator -- largely because they believe it would backfire -- and they hope other Democratic rivals will assume that role.

This week, Biden is traveling to New Hampshire, which will be a critical battleground between the two leading candidates.

"You know how difficult it is to be the frontrunner from the start and maintain that over time," said Lou D'Allesandro, a longtime New Hampshire Democratic legislator and top Biden supporter in the state. "There are always ups and downs, but we're holding our own. And give her credit where credit is due, but by the same token, we've got to work harder."

Biden's advisers have acknowledged Iowa and New Hampshire could be tough terrain for his candidacy, but they routinely emphasize his appeal in South Carolina, particularly among black voters in the fourth nominating state; A CNN South Carolina poll released last month found he had a huge lead over his opponents -- 37% over Warren's 16% and Sanders' 11%. His team is also building out its operations in Super Tuesday states, with announcements for key campaign organizers expected this week, in hopes of building a firewall in states with more minority voters to help slow Warren's momentum if she wins early contests.

"We have a broader base and coalition than anyone else," said Pete Kavanaugh, deputy campaign manager for Biden who is overseeing early-state contests. "Once you get past South Carolina, it's a delegate game."

But in conversations with more than a dozen campaign advisers and Biden loyalists, it is the subject of Hunter Biden that comes up again and again as the most worrisome aspect of the moment. He is seen by many inside Biden's orbit as something of the former vice president's kryptonite, who presents unique and uncertain challenges.

On the campaign trail, Biden's discussion of his son and his business dealings have been limited. Biden bristled at a recent question about whether his son's position on the board of a Ukrainian gas company -- at the very time the former vice president served as the point man on Ukraine in the Obama administration -- presented a potential conflict. There is no evidence of wrongdoing by either Joe or Hunter Biden.

"There has been no indication of any conflict of interest from Ukraine or anywhere else. Period," Biden told reporters, his voice raising. "I'm not gonna respond to that. Let's focus on the problem. Focus on this man, what he's doing as President that no president has ever done."