(CNN) Senate Democratic Leader Chuck Schumer stepped to the microphone to rally a crowd of President Donald Trump's opponents in New York's Battery Park on Sunday.

"Are we gonna win this fight?" he asked.

The cheers Schumer got back were mixed with jeers. "Stop voting for his nominees!" an attendee shouted back.

The episode showed the pressure Democratic senators face as they head into another week of votes on Trump's Cabinet nominees.

Democrats have watched as progressives turned out en masse at pro-Obamacare rallies, then stunned the political world with the attendance across the globe at women's marches, and now are opposing Trump's executive order banning travel to the United States from seven Muslim-majority nations with protests at airports across the the country.

The protesters' and activists' loyalty, though, is to their causes -- not to Democrats -- and what binds them is their strident opposition to Trump. They are demanding total opposition to the President's Cabinet nominees, and turning their fury on Democrats who don't fight Trump tooth and nail.

On Monday, Schumer outlined the Cabinet picks he would vote "no" on , in a Facebook post.

"Rep Mick Mulvaney for Budget Director, Rep Tom Price for Health and Human Services, Steve Mnuchin for Treasury, Scott Pruitt for EPA and Andy Puzder for Labor have repeatedly shown they will not put the American People or the Laws of our nation first, and I will vote against their confirmations."

Even the party's liberal icons like Sen. Elizabeth Warren of Massachusetts aren't getting the benefit of the doubt.

Warren's committee vote to confirm Ben Carson for secretary of Housing and Urban Development set off intense backlash on the left -- leading to Warren addressing her vote in a Facebook post that began with the frustrated line: "OK, let's talk about Dr. Ben Carson."

Schumer also said he wouldn't back Trump's choices for education secretary, state and attorney general.

"Yes, I adamantly disagree with many of the outrageous things that Dr. Carson said during his presidential campaign. Yes, he is not the nominee I wanted," Warren wrote. "But 'the nominee I wanted' is not the test."

Some Democrats are attempting to strike an impossible balance: The left craves the same tactics Senate Republican Leader Mitch McConnell used to stymie President Barack Obama's legislative agenda and block him from filling a Supreme Court vacancy.

But Senate Democrats have also sought to pick their battles, knowing that one day Republican senators could face the same pressures to oppose a Democratic president.

Tying nominees to executive order

On deck Monday is a Senate vote to advance the nomination of former ExxonMobil CEO Rex Tillerson to become secretary of state.

Democrats are now expected to push for the vote to be delayed until he comments on the Trump travel ban on refugees and citizens of seven Muslim-majority countries.

Democrats say this is going to be a big line of focus going forward, hoping to to put the question to all the nominees on whether they support the executive order. This includes non-controversial nominees, including Elaine Chao, Senate Majority Leader Mitch McConnell's wife, who was chosen to head the Department of Transportation and would have oversight on the airline industry/airports.

Alabama Sen. Jeff Sessions, Trump's pick for attorney general, energy secretary nominee Rick Perry, the former Texas governor, Rep. Ryan Zinke, Trump's Interior Department pick, and education secretary nominee Betsy DeVos are all slated for committee votes Tuesday.

Trump could also roll out a Supreme Court nominee as early as Tuesday, setting off another battle royale on Capitol Hill.

Virginia Sen. Tim Kaine -- the 2016 Democratic vice presidential nominee -- tweeted a passionate criticism of Trump on Saturday, saying the United States should not "turn our backs on widows and orphans fleeing the very evil we despise."

Then a response came from Howard Dean, the former Democratic National Committee chairman and progressive hero.

"Tim, this is great but the Dems in the Senate actually have to do something about this stuff. You are being left behind by your base," Dean wrote.

Tim, this is great but the Dems in the Senate actually have to do something about this stuff. You are being left behind by your base https://t.co/Ul5K4nzmqe — Howard Dean (@GovHowardDean) January 29, 2017

Kaine defended himself Sunday on NBC's "Meet the Press," arguing that opposition to Trump's Cabinet nominees is so fierce in part because of Democrats' tough questioning.

"We are holding Trump nominees' feet to the fire, demonstrating to the world that many of them are either unqualified or extreme or ethically challenged. And I'll tell you, Chuck, I have never seen calls to my office from folks the way I've seen them over these cabinet nominees," Kaine told host Chuck Todd. "And that's because a lot of us on the Democratic side are cast in a spotlight on what they're doing."

The real test of Democrats' reading of the national mood, though, will be a set of five red-state senators up for re-election in 2018: Missouri Sen. Claire McCaskill, Indiana Sen. Joe Donnelly, Montana Sen. Jon Tester, West Virginia Sen. Joe Manchin and North Dakota Sen. Heidi Heitkamp.

Dean wasn't the only Democrat calling on the party's senators to block Trump's nominees.

Dan Pfeiffer, a long-time top Obama aide, tweeted that Democrats need to oppose Trump nominees including Sessions.

"We can't live in a world where Trump violates every norm and Democratic elected officials support people like Sessions out of courtesy," he said.

We can't live in a world where Trump violates every norm and Democratic elected officials support people like Sessions out of courtesy https://t.co/Li1pkuX18P — Dan Pfeiffer (@danpfeiffer) January 29, 2017

In Battery Park on Sunday, Linda Sarsour, a Palestinian American activist and former Bernie Sanders campaign surrogate, said that any Democrat who voted to confirm Sessions should expect a primary challenge next time they're on the ballot.

"That's not a threat," she said. "It's a promise."