Trump goes after Biden — and against advisers' advice

That's exactly the behavior several of the President's political advisers have been warning him against, wary that Trump will elevate a potentially formidable rival, two sources familiar with the discussions told CNN.

"Sleepy Joe Biden is having his first rally in the Great State of Pennsylvania. He obviously doesn't know that Pennsylvania is having one of the best economic years in its history," Trump tweeted. "The Dues Sucking firefighters leadership will always support Democrats, even though the membership wants me. Some things never change!"

Within hours, the former vice president fired back, showing just why Trump's advisers might be concerned..

"I'm sick of this President badmouthing unions. Labor built the middle class in this country. Minimum wage, overtime pay, the 40-hour week: they exist for all of us because unions fought for those rights. We need a President who honors them and their work," Biden tweeted, engaging in the mano a mano Twitter fight many of his rivals would relish.

Don't get sucked in

The President has been advised in recent weeks not to get sucked into a one-on-one verbal brawl with any of the top contenders for the Democratic presidential nomination, mindful that squaring off with any of the contenders at this early stage could help elevate them in the eyes of Democratic voters and give them more oxygen to rise above the crowded pack. Those advisers, though, knew it was only a matter of time before Trump would do just that.

That advice has been especially true for taking aim at Biden, whom many Republican operatives -- and Trump himself -- believe would pose a significant threat to the President should he win the Democratic nomination.

Trump campaign operatives have been cautious not to weigh in on which candidate concerns them most as a general election nominee. And with Democratic candidates eager to prove that they are best positioned to beat Trump, several of the President's political advisers have cautioned him not to play into their hands by responding to their attacks at this early stage.

While the Trump campaign has released statements knocking top contenders as they entered the race, aides have said the campaign doesn't plan to go after specific candidates as their primary unfolds. Campaign aides also acknowledge that the President is the campaign's ultimate top strategist and if the President decides he wants to switch gears, the campaign will follow suit.

Trump, who has privately been unnerved at the prospect of a Biden candidacy, has struggled to resist getting drawn in by Biden's allure and his attacks since the former vice president officially entered the presidential race last week.

After Biden launched his campaign by focusing on the President's response to white supremacist demonstrations in Charlottesville, Virginia, Trump added fuel to the fire by defending his response once again -- this time saying he answered "perfectly" and reigniting a debate about his response, which prompted criticism even from fellow Republicans.

"If you look at what I said you will see that that question was answered perfectly," Trump told reporters Friday, before praising the former Confederate Gen. Robert E. Lee as "one of the great generals."

And then came Monday's string of tweets.

Bring on Biden?

Not all of the President's allies and advisers are concerned about Trump elevating Biden.

One Trump adviser pointed out that Biden is "already polling at No. 1 or 2" in the Democratic field.

Jason Miller, a former top communications adviser to the Trump campaign and transition, said Trump was right to take shots at Biden on Monday.

"Everyone in the media is going to be covering today's Joe Biden event and they're going to be talking about Joe Biden, so why miss the opportunity to help frame the debate?" Miller said.

Miller also acknowledges he is in a "contrarian group" of strategists who believe Trump would be lucky to square off against Biden in the general election.

"I believe Joe Biden is the dream candidate that Donald Trump should want to run against in 2020," Miller said. "Biden is a recycled political candidate much in the same sense as former Secretary (Hillary) Clinton and Trump will be able to use Biden's 47 years in office as a massive blunt instrument to hit Biden over the head with again and again. Joe Biden being the Democrat's nominee allows Trump to be the change agent in 2020 even though he's the incumbent."