Senate Majority Leader Mitch McConnell (Ky.) and other Republicans say the chamber will hold no hearings and no votes this year on President Obama’s expected nominee to replace the late Supreme Court Justice Antonin Scalia.

Dozens of left-leaning interest groups — including unions, civil rights, LGBT, women’s and lawyers’ organizations  —are engaged in an intense and burgeoning effort to force Senate Republicans to consider President Obama’s Supreme Court nominee.

For now, many groups’ early strategy is not to float specific names they’d like to see nominated to the court, but to attack Senate Majority Leader Mitch McConnell’s (R-Ky.) vow to block confirmation hearings altogether. Republicans on the Senate Judiciary Committee insist they won’t consider Obama’s candidate no matter their politics.

The liberal movement is still coalescing and it is not yet clear how much various groups will spend — together or separately — to argue the Senate should consider Obama’s choice to replace the late Justice Antonin Scalia. But groups are already casting a wide net, targeting Republican senators’ reelection campaigns, penning op-eds, circulating petitions, and promoting the Twitter hashtag #DoYourJob — a jab aimed squarely at Senate Republicans.

“We’re just getting started but what’s clear is this is a shared concern, and in some instances defy party labels,” said Wade Henderson, president and chief executive of the Leadership Conference on Civil and Human Rights. “People want to get this process moving.”

[Republicans vow no hearings and no votes for Obama’s Supreme Court pick]

The AFL-CIO called the Judiciary Committee’s refusal to consider an Obama nominee “a blatant dereliction of duty undertaken simply to hold a seat on the Supreme Court open in hopes of a Republican winning the presidency.” An AFL-CIO spokeswoman said the union “will continue to put pressure on Republicans in various ways,” but did not elaborate on specific steps.

As the nomination battle escalates, liberal interest groups could play an extremely important role in a competitive election year in pressuring moderate Republicans to consider Obama’s candidate. They could also stoke the ire of the base, which would likely help Democrats turn out in higher droves in November.

The liberal front could also become divided — or enraged, if the president nominates a centrist or even a Republican candidate, though Nevada Gov. Brian Sandoval withdrew from contention on Thursday  — as groups’ interests diverge.  For now, the groups seem to be rowing in the same direction by arguing the Senate has a constitutional duty to consider Obama’s candidate.

[Nevada GOP Gov. Brian Sandoval withdraws from Supreme Court contention]

On Wednesday, several progressive groups including Credo, Moveon.org and People for the American Way delivered 1.3 million petition signatures to the Senate, denouncing Senate Republicans’ blockade on hearings.

Credo plans to launch digital ads, starting with social media ads, pressuring Republican leaders and senators in swing states not to obstruct the president’s nominee, but has yet to finalize its budget for the campaign.

The ads will target McConnell (R-Ky.), Senate Judiciary Chair Chuck Grassley (R-Iowa), Sens. Kelly Ayotte (R-N.H.), Ron Johnson (R-Wisc.), Rob Portman (R-Ohio), Pat Toomey (R-Pa.), Lisa Murkowski (R-Alaska), John McCain (R-Ariz.), Roy Blunt (R-Mo.), and GOP presidential candidates Ted Cruz (R-Tex.) and Marco Rubio (R-Fla.)

EMILY’s List, a group that backs Democratic women candidates, is accelerating efforts to oust Toomey, McCain and Ayotte by supporting their opponents in the November election. All three senators have said the next president, not Obama, should appoint a replacement for Scalia. The group was already backing those senators’ rivals, but is now promoting editorials and Tweets critical of Ayotte and McCain.

The group is also seeking donations “to make sure Hillary Clinton is picking the next justice and we have a Democratic Senate to confirm them,” one fundraising email said.

The Leadership Conference on Civil and Human Rights, a group influential in judicial nominations, is mobilizing its network of retired judges, former prosecutors and state bar presidents to urge citizens — particularly in districts where lawmakers have vowed not to consider an Obama nominee — to press their member of Congress to reconsider.

The conference is working with several other legal organizations including the Lawyers’ Committee for Civil Rights Under Law, Alliance for Justice and Lambda Legal. Lambda Legal, which supports LGBT equality, has gathered 4,000 signatures for a petition it plans to send Grassley and Judiciary top Democrat Patrick Leahy (Vt.), demanding that the Senate hold a hearing and vote.

The conference and its allies are also reaching out to business leaders in hopes of building a broader network. They hope companies may be swayed because they believe split Supreme Court decisions will cause confusion over how to implement workplace policies and other business practices.

On Tuesday, four Democratic former U.S. attorneys published an op-ed in the Cincinnati Enquirer, saying that delaying a successor would be “unsafe” because uncertainty over the law impedes law enforcement’s ability to protect the public.

“Unsettled legal questions regarding search and seizure, digital privacy and federal sentencing are either pending before the Supreme Court or headed there,” the editorial says. “It is unfair and unsafe to expect good federal agents, police and prosecutors to spend more than a year guessing whether their actions will hold up in court. And it is just as unfair to expect citizens whose rights and liberties are at stake to wait for answers while their homes, emails, cell phones, records and activities are investigated.”

The piece was written by Steve Dettelbach, Jenny Durkan, Melinda Haag and Tim Heaphy, the former U.S. Attorneys for Northern Ohio, Western Washington, Northern California and Western Virginia, respectively.

Similarly, constitutional legal scholars criticized the Senate and warned of the consequences of having a split court for an extended period of time.

“The Senate announcing it wouldn’t hold hearings violates its Constitutional duties,” said Erwin Chemerinsky, dean of U.S. Irvine School of Law. “I can’t identify any other instance where the Senate Judiciary Committee wouldn’t even hold a hearing. It’s unprecedented to say they wouldn’t even consider confirmation before someone is nominated for the slot.”