Washington (CNN) President Donald Trump enters the second week of his presidency facing a growing political backlash -- with protesters in the streets, lawsuits mounting and his own party fracturing over his executive order banning travel to the United States from seven Muslim-majority nations.

The resistance is offering an early and immediate preview of the dynamics of the Trump presidency: It tests the opposition's strength and durability, the White House's crisis management capabilities and Capitol Hill Republicans' willingness to stomach the controversy that accompanies Trump's efforts to fulfill his campaign promises.

Meanwhile, stories of students, public figures and even a military translator who are suddenly unclear on whether they can enter the United States are setting social media ablaze.

It all comes as the nascent Trump administration enters a critical period, with Trump still seeking Senate confirmation for most of his Cabinet nominees.

The White House is scrambling to tamp down the controversy, with Trump addressing it in a statement and taking a warning shot at critical Republicans. And his administration is considering moving up the announcement of his first Supreme Court appointment from Thursday to possibly Tuesday, potentially in an effort to change the subject, one source told CNN.

Trump on defense

Trump released a statement defending his ban Sunday evening, while also lashing out at two Republican senators who had opposed it and the news media over its coverage of the ban.

"America has always been the land of the free and home of the brave. We will keep it free and keep it safe, as the media knows, but refuses to say," Trump said in the statement.

He continued: "To be clear, this is not a Muslim ban, as the media is falsely reporting. This is not about religion -- this is about terror and keeping our country safe."

Republican backlash

In a joint statement, Arizona Sen. John McCain and South Carolina Sen. Lindsey Graham earlier Sunday had called Trump's travel ban a "self-inflicted wound in the fight against terrorism."

"This executive order sends a signal, intended or not, that America does not want Muslims coming into our country. That is why we fear this executive order may do more to help terrorist recruitment than improve our security," the two said.

Trump lambasted McCain and Graham together in a two-tweet response, writing: "The joint statement of former presidential candidates John McCain & Lindsey Graham is wrong - they are sadly weak on immigration. The two Senators should focus their energies on ISIS, illegal immigration and border security instead of always looking to start World War III."

The joint statement of former presidential candidates John McCain & Lindsey Graham is wrong - they are sadly weak on immigration. The two... — Donald J. Trump (@realDonaldTrump) January 29, 2017

...Senators should focus their energies on ISIS, illegal immigration and border security instead of always looking to start World War III. — Donald J. Trump (@realDonaldTrump) January 29, 2017

But even as Trump hit McCain and Graham, other Republicans were similarly criticizing his executive order.

Rep. Will Hurd, R-Texas, called it "the ultimate display of mistrust." Senate Foreign Relations Committee Chairman Bob Corker, R-Tennessee, said the order "has been poorly implemented, especially with respect to green card holders."

"This was an extreme vetting program that wasn't properly vetted," Sen. Rob Portman, R-Ohio, told CNN's Jake Tapper on "State of the Union."

Legal battles mount

Already, a federal judge in New York blocked part of Trump's executive order on immigration, ruling that authorities could not remove individuals from seven Muslim-majority countries who had arrived in US airports after the order had been issued. Other judges had ruled against the order, as well.

Sixteen Democratic state attorneys general issued a joint statement calling Trump's move "unconstitutional, un-American and unlawful" and vowing to fight it in court.

The controversy comes the week Trump has said he will announce his choice for a vacancy on the Supreme Court.

Democratic House and Senate leaders have planned a protest outside the Supreme Court for 6 p.m. ET Monday.

The chaotic scenes around airports Saturday came in part because Trump's administration had reportedly not allowed career Homeland Security Department staff to see the executive order.

One key question for many is how the order will affect US green card holders and people who hold dual citizenship with a Trump approved country and one of the seven banned nations.

Adding to the confusion, Trump administration officials seemed to at times contradict themselves during appearances on Sunday news shows. In mere minutes during an interview with NBC, White House chief of staff Reince Priebus said the order "doesn't affect" green card holders, then later said "of course" it affects green card holders from Iran, Iraq, Syria, Sudan, Libya, Yemen and Somalia -- the seven countries Trump has temporarily stop immigration from for 90 days.

Later Sunday, Homeland Security Secretary John Kelly issued a statement that sought to clarify their status saying, "lawful permanent resident status will be a dispositive factor in our case-by-case determinations."

Another Homeland Security official told CNN the green card holders who are returning to the US will still go through additional screening and national security checks upon landing. However, the government is trying to ease their entry back into the US. Unless they have a significant criminal history or links to terrorism, they will be allowed back in the country after going the check the official said.

"This is our message to them: get on a plane. Come back to the US. You will be subject to secondary screening, but everything else will be normal," the Homeland Security official told CNN.

Protests fill airports nationwide

Hordes of protesters gathered at airports across the United States, carrying signs, welcoming international arrivals and chanting anti-Trump slogans.

In the second weekend of Trump's presidency, it was the second weekend in a row of mass protests -- following on the heels of anti-Trump women's marches in Washington and cities around the world.

And the protests extended beyond airports. Throngs of people were gathering Sunday afternoon outside the White House. Crowds also were forming in Boston's Copley Square, at Battery Park in Manhattan and at airports in Atlanta, Los Angeles, Washington and Dallas, with more planned elsewhere.

Top Democratic officials were involved in the protests, too.

In San Francisco, Democratic National Committee chair candidate Tom Perez was on Facebook livestreaming his participation in protests there.

New York Gov. Andrew Cuomo ordered the Port Authority of New York and New Jersey to reverse an earlier decision to restrict passage aboard the JFK Airport AirTrain to ticketed passengers and airport employees only.

He also instructed state police and the Metropolitan Transportation Authority to assist with security and transportation for protesters.

"The people of New York will have their voices heard," Cuomo said.

New York Mayor Bill de Blasio posted a series of tweets calling the travel ban "shameful" and "simply un-American." He later tweeted a photo of protesters Sunday at New York's Battery Park, saying: "There is something more important and powerful than all three branches of government. It is you -- the people. #BatteryPark."

There is something more important and powerful than all three branches of government. It is you -- the people. #BatteryPark pic.twitter.com/FXVHlahxHB — Bill de Blasio (@NYCMayor) January 29, 2017

Chelsea Clinton even got in on the act, tweeting a picture of protesters in New York: "Yes. We will keep standing up for a country that matches our values and ideals for all."

Yes. We will keep standing up for a country that matches our values and ideals for all. pic.twitter.com/yfVlX5sL3f — Chelsea Clinton (@ChelseaClinton) January 29, 2017

Virginia Gov. Terry McAuliffe joined protesters at Dulles International Airport outside Washington.

"This executive order is antithetical to the values that make America great, and it will make our country less safe," he said in a statement.