Rain or shine, there will be cake, and on Wednesday, huddling underneath umbrellas, the group of labor rights activists carried their latest to Sen. Mark R. Warner’s doorstep in Alexandria, Va.

It was the kind of white sheet cake typically found at children’s birthday parties — the seventh they have delivered to Warner’s home on consecutive Wednesdays, each made by a union-member baker and decorated with a slogan urging Warner to co-sponsor the Protecting the Right to Organize Act.

“Support the president,” the icing said, next to cutout pictures of Joe Biden. And then, partly quoting him: “Send me the PRO Act.”

They knocked on Warner’s door three times around 8:15 a.m. No answer.

So they set the cake on the doormat, then retreated back across the street with their signs — wondering what it would take to get the three-term Democratic senator to line up behind what they consider the most monumental piece of labor rights legislation in decades.

“We have tried vanilla, we have tried chocolate. Someone has suggested an ice cream cake,” said Virginia Diamond, head of the Northern Virginia Labor Federation, the local arm of the AFL-CIO. “So we are not sure what it will take. But we have a friendly relationship with the senator . . . and we do believe that when he talks to people he respects, he will come around and understand what is at stake.”

Warner, a former Virginia governor and business executive, is one of only three holdouts in the Senate Democratic caucus who have yet to co-sponsor the Pro Act, despite feverish lobbying by unions. The others are Arizona Sens. Mark Kelly and Kyrsten Sinema. Some labor groups have threatened to pull their support for those three Democrats unless they co-sponsor the bill, and Diamond said the Virginia AFL-CIO, which had long backed Warner, did not endorse him in his race against Republican Daniel Gade last year.

President Biden last week added to the pressure when he called on the Senate to pass the bill during his address to a joint session of Congress, saying “The middle class built this country, and unions built the middle class.”

Roxana Mejia, of the International Union of Painters and Allied Trades District Council 51, said she had been knocking on doors to support Warner for years. Now here she was, knocking on his.

“He’s always told us he’s stayed with workers — this is the time to do it,” she said.

The Pro Act, which passed the House in March, would loosen restrictions on certain types of strikes, penalize employers for retaliation against workers who organize and allow more workers currently classified as independent contractors to join unions and access benefits, if they want.

It would also weaken states’ right-to-work laws — including in Virginia — a change that would allow unions to negotiate with companies to require employees to pay “fair-share” fees to fund union representation during disputes. Efforts by liberal lawmakers in Richmond to repeal Virginia’s right-to-work law have failed, even with the new Democratic majority in both chambers of the legislature.

Republican opposition to the Pro Act in Congress gives the bill dim odds in the Senate, where the filibuster requires the support of 60 senators for legislation to advance. But activists are nevertheless trying to build momentum by lobbying the Democrats who have yet to sign on.

In a combination of written statements and comments during a media briefing this week, however, Warner said he supports “the majority” of provisions in the Pro Act — giving the labor activists reason to believe their diplomatic cake deliveries may not be in vain.

Warner has not been supportive of previous efforts to repeal right-to-work laws. But a spokeswoman said “it’s increasingly his view that all of the workers who benefit from negotiations with management ought to be making some contribution to those hard-fought efforts.”

Still, Warner said certain parts of the bill give him pause. He cited concerns about the provision of the Pro Act that would change how workers are classified as independent contractors or employees, for the purpose of collective bargaining.

Warner said he feared the new classification rules could negatively affect self-employed people’s need for flexibility in a changing economy, particularly for gig workers.

“The notion of long-term permanent work is fundamentally changing,” Warner said. “My fear is that parts of the Pro Act try to fit all work into kind of a 20th century, classic W-2 employment status.”

He has been instead pushing a “portable benefits” model that would allow gig workers, freelancers or other self-employed people to access benefits that would follow them from job to job, regardless of their employer.

Some activists and congressional Democrats say that model would not conflict with the Pro Act. If anything, said Rep. Andy Levin (D-Mich.), vice chair of the House Committee on Education and Labor, the Pro Act would give gig workers more flexibility, allowing them to negotiate any number of benefits models in contracts.

“This is just about giving those workers some power,” said Michelle Woolley, head of the Coalition to Repeal Right-to-Work. “This doesn’t upend the gig worker economy. . . . Those workers are the least powerful in our economy.”

The advocates have never seen Warner himself when they drop off their cakes. In past weeks, his wife, Lisa Collis, or their daughter, sometimes brought the box inside.

On Wednesday, once again, the front door eventually swung open, and Collis smiled and waved.

“We’re not going to eat it,” she yelled across the street to the demonstrators. “But thank you!”

She grabbed the newspapers, and left the cake sitting in the rain.

“It could be that they’re on a diet,” Diamond suggested to fellow organizers. “Should we try something less caloric?”