The words “liberal plot” have not been written or said, as far as I know. However, Justices Thomas and Alito, more so Alito, have consistently ruled against stays of executions, have upheld shorter windows from sentencing to execution, do not find mitigating factors, racial and other biasing, ineffective counsel, or court errors to warrant execution stays. Most relevantly, they have classified many (if not most) execution stay requests as “dilatory litigation” meant to delay without merit, despite other Justices finding merit and, in some cases, granting or upholding the stay, and have given opinions that petitions on the grounds of overly painful execution methods being cruel and unusual as “guerilla war” against capital punishment. I would say it is reasonable to infer that they see “most litigation” as a tactic or “plot” and not legitimate legal concerns. See below for some excerpts, and read [4] and [5] for brief summaries of their crime related opinions.
> “Those who oppose the death penalty are free to try to persuade legislatures to abolish the death penalty. Some of those efforts have been successful. They’re free to ask this court to overrule the death penalty. But until that occurs, is it appropriate for the judiciary to countenance what amounts to a guerrilla war against the death penalty, which consists of efforts to make it impossible for the states to obtain drugs that could be used to carry out capital punishment with little, if any, pain?” Supreme Court Justice Samuel Alito [1]
[1] https://www.huffpost.com/entry/alito-death-penalty-guerrilla...
> During his 15-year career on the U.S. 3rd Circuit Court of Appeals, Alito participated in 10 capital cases. Five were decided unanimously by three-judge panels and involved fairly straightforward issues. The other five provoked strong differences of opinion between Alito and his colleagues. In every one of the five contested cases, Alito voted against the inmate and issued an opinion. Individually and especially as a whole, these opinions show a troubling tendency to tolerate serious errors in capital proceedings.
> Although O’Connor’s approach to capital punishment has been solidly conservative, she has at times supplied a crucial vote in contentious cases in favor of greater care and fairness in the application of the death penalty. Yet it is precisely in the most contentious cases that Alito has shown an unbroken pattern of excusing errors in capital proceedings and eroding norms of basic fairness. [2]
[2] https://www.latimes.com/archives/la-xpm-2005-nov-27-oe-liu27...
> In Murphy’s case, Justice Alito, joined by Thomas and Gorsuch, accused defense lawyers of “inexcusably dilatory litigation tactics” and complained that “the great majority” of applications for stays of execution “are almost all filed on or shortly before the scheduled execution date … [with] no good reason for the late filing.” Staying Murphy’s execution, Alito wrote, “countenance[es] the dilatory litigation [and], I fear, will encourage this damaging practice.” While acknowledging that “[t]he claims raised by Murphy and Ray are important and may ultimately be held to have merit,” Alito said that “[p]risoners should bring such claims well before their scheduled executions so that the courts can adjudicate them in the way that the claims require and deserve and so that States are afforded sufficient time to make any necessary modifications to their execution protocols.” [3]
[3] https://deathpenaltyinfo.org/news/death-penalty-opinions-exp...
[4] https://www.ontheissues.org/Court/Samuel_Alito_Crime.htm
[5] https://www.ontheissues.org/Court/Clarence_Thomas_Crime.htm