The latest tweets came this afternoon, when Trump singled out Reps. Raul Labrador, R-Idaho; Mark Meadows, R-North Carolina; and Jim Jordan, R-Ohio, who are all members of the Freedom Caucus.
Those tweets came hours after Trump tweeted that the caucus, which largely opposed the Republican health care bill last week, will do damage to the Republican Party as a whole.
At today's press briefing, Spicer said Trump's tweet is "consistent with everything he has said since Friday of last week."
"His comments and his tweets speak for themselves," Spicer said.
The second round of tweets came later, when Trump wrote "If @RepMarkMeadows, @Jim_Jordan and @Raul_Labrador would get on board we would have both great healthcare and massive tax cuts & reform."
He followed that with another tweet, asking where the three congressmen were on the issue.
This is not the first time that Trump has singled out the Freedom Caucus. He addressed the faction on social media two days after the bill was shelved.
Members of the caucus largely dismissed Trump's thinly veiled threats to challenge their re-election efforts in 2018.
"I mean, it's constructive in fifth grade," Rep. Justin Amash, R-Michigan, a founding member of the Freedom Caucus, sarcastically told reporters at the Capitol today when asked if Trump's pressure could reignite negotiations.
"I'm not going to get hung up on a tweet," Rep. Scott DesJarlais, R-Tennessee, said in an interview.
"My impression of the White House doesn't come from Trump's tweets," said DesJarlais, who was courted by Trump on the health care bill but planned to vote against it. "He [tweets]. I don't really pay much attention to it."
Rep. Trent Franks, R-Arizona, who was open to supporting the health care bill last week, said Freedom Caucus members are "the best friends the president has" on Capitol Hill.
"If a primary challenger will serve this country better than me, I'm certainly willing to entertain that," said Franks, a veteran lawmaker.
Sen. Bob Corker, R-Tennessee, the chairman of the Senate Foreign Relations Committee, took a dig at House Speaker Paul Ryan of Wisconsin after he suggested in a CBS interview that he was concerned Trump would work with Democrats over conservative Republicans after the failure of the health care bill.
"We have come a long way in our country when the speaker of one party urges a president NOT to work with the other party to solve a problem," Corker tweeted.
ABC News' Katherine Faulders contributed to this report.