He tweeted, "Getting more bad info @RandPaul. Don't screw up #TaxReform now. You already saved #Obamacare by trashing #GrahamCassidy-Heller-Johnson."
Graham continued: "Point #2: The Budget resolution doesn't affect statutory spending caps."
Graham was responding to Paul's tweets, who wrote: "Senators (John) McCain and Graham are torpedoing the budget by insisting on busting the budget caps for more spending. I have told the White House and GOP leaders that if they simply stick to their own caps, the rest of the Budget is fine and I'll vote yes. It is a simple, but important, change they could easily make. The ball is in their court."
The GOP-controlled Senate voted 50-47
on Tuesday to begin debate on the 2018 budget resolution, a procedural step toward laying the groundwork for passing tax reform.
On Tuesday's procedural vote, McCain and Paul voted "yes," though neither has committed to supporting the underlying budget resolution.
Graham told CNN he is "100%" yes on the budget and that Paul is conflating the budget with appropriations.
When asked for his response to Paul's argument on Twitter, he called it: "Very disingenuous"
"There is nothing in the budget resolution that affects spending caps," he said.
He said the increased defense spending that he wants happens in the appropriations process, not the budget resolution.
Paul responded to Graham's criticism later Tuesday, saying, "Lindsey Graham wouldn't know a conservative if he met one ... I don't consider him to be a conservative or a bona fide Republican critic."
Both Graham and Paul played golf with President Donald Trump on Saturday and Sunday, respectively. Tuesday's tweets between the senators reveal the two's differences in their own Republican Party, and how Trump is trying to work with both of them.
This story has been updated to include additional developments.