If any Republican senator is thinking about defecting from the GOP’s tough line on blocking a Supreme Court nomination until next year, then let them be warned. Outside conservative groups are preparing to go to war over who should get to pick a replacement for Justice Antonin Scalia, who died unexpectedly over the weekend, and they don’t want to see even a hearing considering the nominee President Obama has vowed to put forward.

“The strategy that makes the most sense is to say that there should not be any consideration of this nominee,” Curt Levey, executive director of the FreedomWorks Foundation, said in an interview with TPM. “It would be irrelevant to have a hearing because it’s the situation: the fact that it’s an election year, the fact that his policies are before the court, the fact that the court is so finely balanced at the moment.”

The pressure he and other groups are putting on lawmakers comes after Senate Majority Leader Mitch McConnell (R-KY) issued a statement almost immediately after Scalia’s death, signaling that Republicans would delay the confirmation process, regardless of the nominee, until after a new president has been inaugurated.

“It’s not about any one particular nominee,” Carrie Severino, chief counsel and policy director of the conservative legal organization Judicial Crisis Network, told TPM. “We know exactly the kind of person [Obama] is going to appoint. Getting into those details is just a silly distraction.”

For both sides of the political divide, the stakes could not be higher.

“We’ve known this was coming for while. We set aside resources for this fight because everyone knows the next president is likely to have maybe three nominations to make,” Severino said. She wouldn’t go into details about her group’s next moves when it comes to halting the Obama nominee, but said “we’re totally prepared for it,” including financing the effort.

One key choice for Republican lawmakers is whether to go through the motions of considering a nominee — though hearings and other vetting — before blocking them in a vote, or whether GOP leaders should refuse to even begin the process in the first place. McConnell’s statement, which was quickly followed by statements made by other Republican leaders echoing his logic, suggested they were planning for a full stonewall — no hearings, no nothing

Outside conservative groups with influence on Capitol Hill — and particularly those that inhabit its far-right flank — were quick to cement the line McConnell drew.

“Senator McConnell is right, under no circumstance should the Republican Senate majority confirm a Supreme Court nominee as Americans are in the midst of picking the next president,” Michael Needham — the head of Heritage Action, the lobby arm of the conservative Heritage Foundation — said in a statement posted Monday.

The Family Research Council is also advocating that Senate refuse to take up any nominee Obama submits.

“The Senate is under no obligation to consider them,” Travis Weber, the director of the FRC’s Center for Religious Liberty, said in an interview with TPM. “President Obama can nominate people until his heart’s content and they have no obligation to look at them one way or another, given the gravity of the moment.”

Some reports have suggested that some Republicans are already wavering on McConnell’s tough line, pointing to comments made by Sen. Thom Tillis (R-NC) and Sen. Ron Johnson (R-WI), but legal activists dismissed that analysis as overstated.

“The headlines about the fracturing are more wishful thinking than anything else,” Severino said. “If you really look at the full statements, I think it’s remarkable how the Republican senators are speaking with one voice on this issue.”

According Levey, FreedomWorks is preparing to target senators who look like they’ll back down from the fight, while bolstering those who hold to McConnell’s tough initial line.

He said his group sent out an alert to its activists across the country Monday evening that resulted in 14,000 emails to McConnell’s office, and that, aside from email pressure, they are planning events in senators’ home states.

Levey also threatened to primary senators who don’t toe the line.

“In some cases where there are potential primary opponents, we might consider supporting a primary opponent if the senator did not do the right thing,” Levey said.

As Rory Cooper, a GOP strategist, wrote on Medium, part of the strategy of denying the Obama administration even a hearing is to prevent the media from focusing on the person instead of the process, and in effect, starving the story of oxygen.

But the outside groups pushing the tactic also argued it’s a more principled approach to blocking a nominee that Republicans will inevitably block in a vote anyway.

“It’s the most honest,” Levey said. ”The very fact that people on our side feel very strongly that there shouldn’t be a hearing before we know the nominee is because it’s not really about the nominee. … Frankly, the real objection here is to Obama.”