On Sunday, retiring Pennsylvania Senator Pat Toomey delivered a stern closing address to his Republican colleagues, claiming that former President Donald Trump's hold on the party is "waning."

Toomey's remarks indicate an ongoing schism within the Republican Party over how to respond to the party's dismal showing in the November midterm elections.

"I have heard from many, many formerly very pro-Trump voters that they think it's time for our party to move on," Toomey said on CNN's "State of the Union."

"So yes, I think that process is underway. ... It's not a flip of a switch, it doesn't happen overnight. He still has a significant following, that's for sure. But I do think his influence is waning," he added.

The Republican party's introspection comes at a crucial time for Trump and the party as a whole.

Republicans narrowly won the U.S. House, falling far short of pre-election projections, while Democrats increased their majority in the U.S. Senate by flipping Toomey's seat in Pennsylvania.

Senate GOP leaders are keen to put the Trump era behind them and pursue candidates who would appeal to more moderate and mainstream suburban voters who defected from the party due to their dislike of the former president.

However, these Republicans face a significant and loud Trump-aligned faction inside their party, particularly in the new House GOP majority. As they urge for the GOP to return to core conservative ideas, a hard-right bloc now wields power over Republican leader Kevin McCarthy in his pursuit of the speakership.

Toomey, a prominent Trump critic who was one of seven GOP senators who voted to convict the former president at his second impeachment trial, said in his parting statement on the Senate floor on Thursday, "Our party can't be about or beholden to any one man. We're much bigger than that. Our party is much bigger than that."

When host Jake Tapper questioned him on Sunday about being referred to as a "Republican in name only" (RINO) because of his criticism of Trump, he maintained his position.

"When Republicans had criticisms of [Trump] - I certainly think mine were valid - that doesn't always sit well with folks who see him as carrying the fight to the other side. So some of that tribalism is built into public political systems anywhere," he said.

"Again, I think, as his influence wanes, the sort of conventional understanding of what words mean kind of gets restored over time. I'm not worried about that," Toomey said.