But not just any Democratic president.

“China is DREAMING that Sleepy Joe Biden, or any of the others, gets elected in 2020,” Trump wrote on Twitter Sunday. “They LOVE ripping off America!”

By Monday afternoon, Biden, making his first trip to New Hampshire since entering the 2020 race, was happily returning fire, criticizing the Twitter-borne blur of threats and flattery Trump had aimed at Beijing. “He’s going about it all the wrong way, a lot of bravado, no action,” the former vice president told reporters.

It is just the sort of fight Biden has been spoiling for: a head-to-head contest with the incumbent on an issue that elevates Biden into a statesmanlike role, well above the Democratic primary fray and all the sniping candidates and liberal litmus tests therein.

For Trump’s advisers, it was one more example of the president’s inability to resist offering what amounts to an in-kind contribution to a Democrat who, according to their own polling, is positioned to soundly defeat them next year.

The president, though, has told advisers he believes he can portray Biden, a longtime Washington veteran, as representative of an ossified political class the same way he did Hillary Clinton, wounding him with enough attacks and put-downs that Biden will either stagger into the general election or collapse in the primary.

In the three weeks since Biden announced his candidacy, Trump has tried out two nicknames on him, accused his opponent and family members of corrupt dealings with Ukraine (prompting a coordinated Democratic response) and argued that he is naïve about the threats America faces.

Early this month, as Biden began his campaign with the endorsement of the firefighters union, Trump unleashed a barrage of almost 60 tweets and retweets about his own support from rank-and-file union members, signaling his anxiety about Biden’s standing with a crucial constituency. Aides have said that Trump is keenly aware that he won in 2016 with support from union voters who did not follow their leaders in backing Hillary Clinton.

But after all that, he then likened Biden’s bid to his own 2016 campaign, in which Trump never relinquished the lead after ascending in the polls, and suggested Biden would probably be the Democratic nominee.

Trump’s attacks on Biden have defied the pleadings of his own aides, who think almost any other candidate would be easier to defeat, and left Republicans puzzled while delighting Biden supporters.

“It just shows everybody that the vice president is the candidate Trump is most concerned about,” said Rep. Cedric Richmond, D-La., a Biden supporter, adding with evident relish: “He just can’t help himself during executive time.”

Matt Gorman, a veteran of past Republican presidential campaigns, said that Trump was simply handing Biden a gift.

“In a Democratic primary, attacks from President Trump are the best thing that can happen to you,” Gorman said. “It elevates you, gives you a huge fundraising boost and sucks the oxygen from your competitors.”

The president’s drumbeat of attacks on Biden have also gotten the attention of congressional Republicans, who would prefer a more easily caricatured boogeyman on top of the Democratic ticket next year. “Bernie Sanders is the perfect guy for us,” said Chris LaCivita, a longtime Republican strategist, referring to the senator from Vermont. “He looks like the professor out of ‘Back to the Future’ and is a hard-core socialist.”

Trump’s offensive has also hastened calls by GOP officials to bring together White House aides, Trump campaign officials and Capitol Hill Republicans in a gathering similar to one last year at Camp David, according to a senior Republican Senate official.

Yet some Democrats, having witnessed how Trump lampooned and eventually bulldozed the Republican field in 2016, are nervous that Trump has shrewdly chosen to define Biden as the front-runner early on, identifying him as the greatest threat in a general election.

Republicans at the super PAC supporting Trump have echoed this theory, telling people in recent weeks that the party must begin eroding Biden’s credibility now and portray him as the picture of a rotten status quo, according to an official at the organization.

Officials at the super PAC, America First Action, have argued that doing so would allow Trump to maintain the outsider image he cultivated during the 2016 campaign, never mind that he is an incumbent president.

But some Republicans close to Trump paint a more simplistic portrait of the president’s actions: That he has simply been consuming cable news coverage about Biden, and firing off tweets based on the coverage and polling on the Democratic race he hears about on the air. And senior Trump campaign aides have recently told other Republican officials that they would rather not face Biden in the general election, according to one party figure familiar with the conversations.

Trump’s aides are not united on the best way to undercut Biden. His initial strength in the Democratic primary has surprised them.

A recent survey of battleground states conducted for the Trump campaign by a leading Republican pollster, Tony Fabrizio, showed Biden handily beating Trump, according to three people briefed on the results. Sanders did not fare as well against Trump in the poll, but also was besting Trump head-to-head in key states., these people said.

Separately, Republicans who are hoping to rescue Sen. Martha McSally of Arizona, one of the party’s most imperiled incumbents, have found Biden leading Trump in that state, which no Democratic presidential candidate has carried since 1996.

Trump has been told about his campaign’s polling, although it was unclear how extensive a briefing he was given. Still, his aides and allies have urged him to stop throwing attention to Biden, arguing that it is better to have the Democrats fight it out and weaken one another over the course of their primary.

”The campaign must force Biden back into the Democratic primary,” said Stephen K. Bannon, the former White House chief strategist. “They’ve allowed him to start a general election strategy unscathed by a potential bear pit created by the populist left. Sanders and Warren are your first lines of defense — and they must be weaponized to attack, especially on China.”

Asked about the president’s focus on Biden, a Trump campaign spokesman, Tim Murtaugh, said they “view the Democrat field as one big socialist organism with more than 20 heads, Joe Biden included.” He then hammered Biden on trade agreements, manufacturing job losses and his comments on the campaign trail in Iowa downplaying China’s threat to the United States.

Trump’s unrelenting attacks have only prompted the former vice president to keep baiting the president, inserting lines into his stump speech he hopes will be picked up by the media and create a new cycle of attack-and-response.

On Monday, in New Hampshire, Biden invoked Trump’s stinging characterization of the state’s opioid difficulties.

“One of the worst statements he made when he was on the phone with the president of Mexico was to refer to New Hampshire as a quote, ‘drug-infested den,’” Biden said in Manchester.

Trump, who has called Biden “Sleepy Joe” and “SleepyCreepyJoe,” has in turn seized on one of the former vice-president’s gaffes, noting that Biden referred to British Prime Minister Theresa May as Margaret Thatcher. “That was a beauty,” the president told Politico last week.

On Tuesday, at a taxpayer-funded and ostensibly policy-focused energy forum in Louisiana, the president asked “What the hell happened to Biden?” and compared him unfavorably to Sanders.

“Bernie’s crazy, but he’s got a lot more energy than Biden, so you never know,” said Trump.

But it is not Sanders who is the focus of attention at the Republican National Committee, which is often directed to act by White House officials. The committee chairwoman, Ronna McDaniel, has used her Twitter account to target Biden multiple times, attacking him for letting “China get away with unfair trade practices” just hours before the president spoke Tuesday.

And last week, the RNC’s research department blasted out an email to reporters with a mountain of opposition research headlined: “Joe Biden Has Made A Career Of Being Soft On China.”

Perhaps most striking, Trump’s personal lawyer, the former New York Mayor Rudy Giuliani, even sought to travel to Ukraine to meet with the country’s president-elect and urge him to pursue an inquiry into the role of Biden’s son, Hunter, in a gas company owned by a Ukrainian oligarch.

Giuliani only backed off after Democrats cried foul. (The Democratic pushback against the aborted mission to Kiev was coordinated by a Biden adviser, Antony J. Blinken, according to a senior Democratic official.)

Trump himself was surprised by Giuliani’s proposed trip, according to Republicans briefed on his thinking, but he has hardly taken a hands-off role on Hunter Biden: The president said last week that a potential Department of Justice investigation into the matter “would be an appropriate thing” for him to discuss with Attorney General William Barr.

This article originally appeared in The New York Times.