In a later tweet, McDaniel called her uncle's commentary "disappointing and unproductive".
"POTUS is attacked and obstructed by the [mainstream] media and Democrats 24/7," she said. "For an incoming Republican freshman senator to attack @realDonaldTrump as their first act feeds into what the Democrats and media want and is disappointing and unproductive."
Until last year, McDaniel had billed herself professionally as Ronna Romney McDaniel. But the former chairwoman of the Michigan GOP dropped her maiden name from most official RNC communications after a request by Trump.
The reactions of Trump and McDaniel followed the publication of an commentary penned by Romney in advance of his swearing-in tomorrow as Utah's junior senator.
In the piece, published online by the Washington Post, Romney said Trump's "most glaring" shortfall has been in shaping the character of the nation.
Romney said he would support Trump policies with which he agrees, but he also pledged to speak out "against significant statements or actions that are divisive, racist, sexist, anti-immigrant, dishonest or destructive to democratic institutions".
Romney wrote: "After he became the nominee, I hoped his campaign would refrain from resentment and name-calling. It did not.
"When he won the election, I hoped he would rise to the occasion. His early appointments . . . were encouraging. But, on balance, his conduct over the past two years, particularly his actions this month, is evidence that the President has not risen to the mantle of the office."
In 2016, Romney, a former Governor of Massachusetts, was a prominent "Never Trumper," calling his fellow Republican a "phony, a fraud".
He adopted a more nuanced view as a candidate for Senate last year, speaking favourably of Trump's actions on taxes and judicial appointments, among others, but saying he did not consider the President a role model for his grandchildren.
Despite Romney's harsh criticism of Trump during the 2016 election cycle, Trump considered Romney for secretary of state but passed him over for Rex Tillerson.
And in February, Trump threw his support behind Romney's Senate bid, writing on Twitter that he would be a "worthy successor" to retiring Senator Orrin Hatch, whom Trump had urged to run for another term.
Trump allies had already taken aim at Romney before the President's tweets today.
"The truth is @MittRomney lacked the ability to save this nation," Trump's 2020 campaign manager, Brad Parscale, wrote on Twitter, adding that "@realDonaldTrump has saved it." Parscale suggested that Romney's op-ed was motivated by jealousy.
During an appearance on Fox News, David Bossie, a senior Trump campaign aide in 2016, said he feared that Romney was positioning himself to be a potent Trump critic in the Senate.
Bossie cited other Republican senators who have spoken out against Trump - Flake, Bob Corker of Tennessee and the late John McCain of Arizona - and said Romney has the potential to play those roles "all in one guy".
Later, Senator Rand Paul, R, also weighed in.
"Like other Big Government Republicans who never liked Reagan, Mitt Romney wants to signal how virtuous he is in comparison to the President," Rand said in a Twitter post.
"Well, I'm most concerned and pleased with the actual conservative reform agenda @realDonaldTrump has achieved."
