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Spicer made the comments at the daily press briefing when Breitbart White House correspondent Charlie Spiering asked for a response to Drudge and "anyone who is worried that the momentum is stalling" on repealing Obamacare and cutting taxes.
"I think it's hardly stalling," Spicer replied. "I think it's a mammoth thing to repeal and replace. I think there's no question to the president's commitment to doing this."
Spicer said that Obamacare is a "big bill" that got "jammed through" Congress when it was passed.
"We can either do it quickly, as the Democrats did, and end up with a monstrosity, where premiums go up and access is limited," he said, referring to repealing and replacing the Affordable Care Act with a GOP solution. "Or we can do it right."
"And I think the president while he wants to get this done as soon as possible and understands what's at stake," Spicer continued. "He wants to do it right. He understands how important health care is to American families and individuals."
"And so his goal is to get it done right and have the outcome it achieves to do," the press secretary concluded. "That's it, plain and simple."
Earlier in the morning, Drudge tweeted that the Republican Party should "be sued for fraud" for not yet delivering on key promises made during the campaign.
"No Obamacare repeal, tax cuts! But Republicans vote to shut Warren?" Drudge tweeted, linking a New York Times article about Republicans voting to silence Massachusetts Sen. Elizabeth Warren.
"Only know how to be opposition not lead!" Drudge added. "DANGER."
The founder and editor of the Drudge Report, a popular conservative news aggregation website, ripped the Republican Party in two follow-up tweets.
"Republican Party should be sued for fraud," he wrote. "NO discussion of tax cuts now. Just lots of crazy. Back to basics, guys!"
In his third tweet, Drudge, a fierce supporter of President Donald Trump, appeared to take a shot at the leadership inside the White House.
"White House eyeing executive order targeting 'conflict minerals' rule ... Meanwhile, is Obamacare penalty tax still in place?" Drudge said.
In recent years, Drudge has become critical of Republican leadership, often taking swipes at House Speaker Paul Ryan, among others.
Criticism of Trump, however, would represent a sharp break from the narrative the conservative-news personality advanced during the campaign. In 2016, Drudge heavily backed the Republican businessman, promoting stories beneficial to his campaign and others harmful to his competitors.