Putting Sen. Tim Kaine on the ticket would betray progressive principles and could actually help Republicans win the White House in November, leading liberal groups warned Hillary Clinton on Thursday as the former first lady prepares to announce her No. 2 over the weekend.

The buzz around Mr. Kaine, first-term Virginia Democrat and the state’s former governor, who has described himself as too “boring” to be vice president, has grown in recent days and reached its height Wednesday night when The New York Times reported that former President Bill Clinton was pushing his wife to pick the senator.

Mrs. Clinton herself in recent days has spoken of her admiration for Mr. Kaine, who by most accounts is qualified for the job and is a broadly popular figure in his key swing state. Yet it also would be seen as the safe, perhaps uninspired, choice.

But progressives argue a Clinton-Kaine ticket would be a train wreck for the Democratic Party and would dampen enthusiasm among hard-core liberals, some of whom finally have come around to Mrs. Clinton for her tack to the left during a long primary battle with Sen. Bernard Sanders.

They specifically cite Mr. Kaine’s support for the Obama administration-backed Trans-Pacific Partnership (TPP), a proposed trade deal that both Mrs. Clinton and Mr. Sanders oppose, as a reason why he shouldn’t be considered. This week, Mr. Kaine also signed a bipartisan letter calling for certain sections of the landmark Dodd-Frank financial regulation bill to be undone. Fourteen other Democratic senators also signed the letter.

“Let’s be really clear: It should be disqualifying for any potential Democratic vice presidential candidate to be part of a lobbyist-driven effort to help banks dodge consumer protection standards and regulations designed to prevent banks from destroying our economy,” said Charles Chamberlain, executive director of the liberal PAC Democracy for America. “With his vote for fast-track authority for the job-killing Trans-Pacific Partnership and this newly uncovered push for bank deregulation, making Sen. Tim Kaine our vice presidential candidate could be potentially disastrous for our efforts to defeat Donald Trump this fall.”

Other progressives suggested that a Kaine pick would indicate that Mrs. Clinton’s supposed shift to the left was merely a short-term political pivot.

“Hillary Clinton’s vice presidential pick will be seen by many as a proxy for how she will govern — boldly or cautiously? The wrong pick could deflate energy among potential donors and volunteers, hurting Democratic efforts to win the White House,” said Stephanie Taylor, co-founder of the Progressive Change Campaign Committee.

Mr. Kaine’s office didn’t respond to questions about his vice-presidential prospects or his support for TPP. On the Dodd-Frank issue, however, a spokeswoman did defend this week’s letter by saying the senator merely wants to loosen restrictions on small community banks and credit unions.

“Sen. Kaine is a strong supporter of Dodd Frank’s financial protections because certain financial institutions wreaked havoc on the American economy … we need strong rules‎to stop that chaos from happening again,” Amy Dudley said in a statement. “He also believes it’s important that the rules are tailored to the character of individual institutions so that we don’t accidentally choke off capital access to the families and small businesses in our communities that create jobs.”

In addition to Mr. Kaine — who joined Mrs. Clinton on a campaign swing through Virginia last week — Labor Secretary Thomas E. Perez, Agriculture Secretary Thomas J. Vilsack and Sen. Elizabeth Warren of Massachusetts are among the other Democrats reportedly under strong consideration.

But more signs point to Mr. Kaine than any other candidate. Mrs. Clinton reportedly wants her pick to have strong national security experience — a box Mr. Kaine would check with his status on the Senate Armed Services Committee. Mrs. Clinton also recently called him a “world-class” lawmaker.

Behind the scenes, Mr. Clinton also is pushing for Mr. Kaine, The New York Times reported Wednesday night, citing sources close to the campaign. Former Clinton Labor Secretary Robert Reich tweeted late Wednesday night that he believes Mr. Kaine will be the pick.

“My bet: Tim Kaine. He’s the safest. And the Hillary campaign is nothing if not cautious,” Mr. Reich said.

Some Clinton supporters argue that Mr. Kaine could help in the swing state of Virginia, and that it’s more important to have a qualified, competent partner than to assuage progressives.

“I think that Sen. Kaine would make a fine choice as her VP pick. I understand that not everyone in the left would be happy, but … the only thing I care about is winning in November,” said Clinton backer Jim Manley, director of the communications practice at QGA Public Affairs and a former spokesman for Senate Democratic Leader Harry Reid.

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