Kennedy is no longer part of the Supreme Court after having chose to retire.
California Senator Kamala Harris announced she is already team #NoKavanaugh.
The Republican president, aiming to entrench conservative control of the court for years to come with the second appointee of his 18 months in office, is expected to choose among two judges with strong conservative credentials: Brett Kavanaugh and Thomas Hardiman.
Before announcing his choice, Trump paused a moment to thank Kennedy for a lifetime of service.
Barrett has been somewhat dismissive of the notion of following Supreme Court precedents, the doctrine known as stare decisis. But if Kavanaugh is Trump's choice, he likely would step away from pending cases.
Mike Sacks, a reporter for the Fox television affiliate in NY and a self-described lapsed lawyer, was among the first to make the connection on Twitter.
"Throughout legal circles he's considered a judge's judge, a true thought leader among his peers", Trump, who named conservative Justice Neil Gorsuch to the court previous year, told an applauding audience in the White House East Room.
Joe Donnelly of Indiana, Heidi Heitkamp of North Dakota and Joe Manchin of West Virginia will be prime targets. They must defend 10 seats in the Senate in states that President Trump won. All three joined with Republicans in confirming Justice Gorsuch.
Reporters and camera crews are staking out the homes of the four finalists, looking for any sign of movement toward an airport, or, in Kavanaugh's case, toward the White House.
If confirmed by the Senate, the Supreme Court swings to the right, granting conservatives another legal victory since Mr Trump became president. Susan Collins of ME and Lisa Murkowski of Alaska, to oppose any nominee who threatens Roe v. Wade.
"Whoever the president selects tonight, if that is from the pre-approved list, everyone ought to understand what it means for the freedom of women to make their own health care decisions and for the protection of Americans with pre existing conditions, those rights will be gravely threatened", said Schumer. "What matters is not a judge's political views but whether they can set aside those views to do what the law and Constitution require", Trump said.
Thai cave rescue: Another boy rescued on Monday, 8 still inside cave
Four more young footballers and their coach at the Mu Pa (WIld Boar) Academy Mae Sai, Ekkapol Chantawong, are still on the ledge. Thai officials have been tight-lipped about the rescue operation, and would not comment on how many people were removed Monday.
Senators are trying to frame the debate before Trump's 9 p.m. announcement.
Neera Tanden, president of the progressive Center for American Progress, says President TrumpDonald John TrumpMichelle Wolf in July Fourth salute: "God bless abortions and God bless America" Graham: Trump's Supreme Court picks "all winners" Man arrested after allegedly threatening to kill Trump supporters, GOP lawmaker MORE is trying to orchestrate a "right-wing takeover" of the judiciary.
With little warning, the Republican administration announced it is freezing payments under an "Obamacare" program that protects insurers with sicker patients from financial losses.
Trump chose Kavanaugh to replace retiring Justice Anthony Kennedy.
Kethledge also was a law clerk to Supreme Court Justice Anthony Kennedy.
Since the 2016 campaign, Trump has made his process for picking Supreme Court justices fairly transparent. He works for the Washington-based lobbying firm Covington & Burling. Jon Kyl would guide the nominee through the confirmation process.
Former New Hampshire Sen. Obama nominated Judge Merrick Garland to replace the late Antonin Scalia, but Senate Majority Leader Mitch McConnell refused to hold a vote on Garland's nomination. He is hoping to replicate his successful announcement of Justice Neil Gorsuch previous year. Bob Casey, D-Pa.
In October of a year ago, Kavanaugh was part of the D.C. Court of appeals that ultimately ruled on an immigrant girl's right to have an abortion while she was in USA custody.
"He could throw a dart on that list" and conservatives would be happy.
All three face gruelling re-election campaigns this year in their conservative states. The race is not expected to be competitive.
Senate rules still leave Democrats with scant options to block confirmation by themselves, though Trump must prevent Republican defections.