Graham (R-S.C.) said Democrats are attempting to "destroy" Kavanaugh over uncorroborated allegations of sexual assault, and confirming him to the Supreme Court is the only "just solution".
"With Leader McConnell's cloture filing, senators have been given ample time to review this seventh background investigation", Shah continued.
At a briefing at the White House, Mr Trump's press secretary, Sarah Sanders, said she did not think the president's performance had made the approval more hard.
Earlier on Tuesday Mr Trump told reporters it was a "very scary time for young men in America when you can be guilty of something that you may not be guilty of".
Kavanaugh's fate remains unclear because three Republicans are undecided: senators Jeff Flake of Arizona, Susan Collins of ME and Lisa Murkowski of Alaska.
"How did you get home?"
They continued: "It is troubling that the Committee Majority has characterized information from Judge Kavanaugh's confidential background investigation on Twitter, as that information is confidential and not subject to public release". "How did you get there?" The much-anticipated report on the sexual assault allegations against the judge was delivered to the Senate overnight where the final vote is now planned for Saturday. "I had one beer - that's the only thing I remember", he stated inaccurately.
A handful of Republicans and Democrats have not decided whether to support Kavanaugh. "He was number one in his class at Yale, he was number one in his law school at Yale, and then what he's gone through over the last three weeks is incredible", he said.
Officials said Trump is seeking to boost Hyde-Smith as close as possible to the 50 percent threshold and lend momentum for a possible runoff.
Meanwhile, Democrats and a few Republicans had raised concerns over the amount of freedom granted to United States federal investigative agency to conduct a lightning-fast probe in a decades old high-level case.
Mr Kavanaugh has denied her accusation as well as allegations by two other women, all dating from the 1980s, while accusing Democrats of a political "hit".
Trump nominated Kavanaugh to replace Anthony Kennedy, who had been a swing vote on a court now divided between four conservative and four liberal justices. Deborah Ramirez, who alleges Kavanaugh exposed himself to her at a Yale party, was interviewed by the Federal Bureau of Investigation, but she told the New Yorker: "People who were key to corroborating my story have not been contacted..." Five of them were connected to Dr. Ford and her story of a 1982 sexual assault at the hands of Kavanaugh.
Flake is a key GOP vote in the confirmation battle, and while he said last week he would vote to confirm Kavanaugh, he also called for an expanded FBI investigation that resulted in a one-week delay. "I categorically and unequivocally deny the allegation by Ford", Kavanaugh said, his voice shaking with anger as he fought back tears. 'I don't know. I don't know. Also interviewed were two others Ford said were present but in a different room: Patrick "P.J".
Outside the US Supreme Court, several hundred people protested against Kavanaugh on Wednesday, carrying signs with messages such as, "We will not be silent" and "I believe survivors".
Shortly after Prof Ford's dramatic testimony to the Senate committee last week, Mr Trump said she was "very compelling" and described her as a "very fine woman".