Sen. Rand Paul Randal (Rand) Howard PaulThe Hill's Morning Report - Sponsored by Facebook - Trump previews SCOTUS nominee as 'totally brilliant' Rand Paul says he can't judge 'guilt or innocence' in Breonna Taylor case Overnight Health Care: Health officials tell public to trust in science | Despair at CDC under Trump influence | A new vaccine phase 3 trial starts MORE's office hit back at fellow GOP Sen. Lindsey Graham Lindsey Olin GrahamSteele Dossier sub-source was subject of FBI counterintelligence probe Hillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Key Democrat opposes GOP Section 230 subpoena for Facebook, Twitter, Google MORE (S.C.) on Tuesday after Graham said the Kentucky Republican wouldn't support an ObamaCare replacement bill.

"While we do have a press assistant opening in the Communications Department, Senator Graham has not applied and should not make public statements on behalf of Senator Rand Paul," said Sergio Gor, a spokesman for Paul.

The pushback came after Graham asserted in speaking with reporters that Paul was "irrevocably gone" and wouldn't support the Senate GOP effort to repeal and replace ObamaCare.

“[Rand's] not going to vote for any bill that has refundable tax credits to help low-income people buy healthcare,” Graham said.

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Paul is one of the most conservative members in the Senate GOP and has pushed for a "full repeal" of ObamaCare.

The Kentucky Republican questioned in a Rare op-ed on Tuesday if the GOP plan is "ObamaCare-Lite," noting that it wants to keep "over ninety percent of the Obamacare subsidies" including helping individuals buy health insurance.

But Paul's spokesman added that the senator is "keeping an open mind" on the Senate healthcare legislation and "remains optimistic the bill can be improved in the days ahead."

If Paul voted against the Senate's legislation, which is still being ironed out, Republicans could only lose one additional senator and still get the 50 votes they need to allow Vice President Pence to break a tie.

No Democrats are expected to support the bill.

The rhetorical back-and-forth comes as a growing number of GOP senators are increasingly pessimistic that they will be able to pass healthcare legislation, even though Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellTrump 'no longer angry' at Romney because of Supreme Court stance On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline The Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power MORE (R-Ky.) said on Tuesday they would be able to move something in the "near future."

Graham separately told reporters on Tuesday that the healthcare bill is "more likely to fail than not."

Tuesday isn't the first time Graham and Paul have exchanged rhetorical barbs. The two are frequently on opposite sides of certain issues, particularly on foreign policy and national security.

After Paul threatened to filibuster former New York City Mayor Rudy Giuliani or former U.S. ambassador to the United Nations John Bolton if they were nominated for secretary of State, Graham knocked the libertarian-leaning senator, saying, "You could put the number of Republicans who will follow Rand Paul’s advice on national security in a very small car."

When Graham criticized Paul's stance on surveillance, where he frequently aligns with Democrats, the Kentucky Republican told Reason magazine that some of Graham's comments don't "rise beyond middle school kind of rhetoric."