WASHINGTON ― The Senate is set to put a bipartisan proposal aiming to ban or force a sale of the popular social media app TikTok on ice, even as the legislation is set to sail through the U.S. House later this week.

It’s not clear if the upper chamber would even take up the bill. Senate Majority Leader Chuck Schumer (D-N.Y.) said Tuesday he would consult with the heads of committees before deciding to put it on the floor, essentially punting on the issue.

The House legislation would ban the app in the United States if its Chinese owners, ByteDance, don’t sell it. Critics of the app have argued that it presents a threat to national security because of its ties to Beijing and how it can be used to spread propaganda. They’ve also expressed concerns with the app’s data privacy given its popularity with millions of American users, many of whom are minors.

“If you don’t think the Chinese Communist Party can twist [TikTok’s] algorithm to make it the news that they see reflective of their views, then I don’t think you appreciate the nature of the threat,” Sen. Mark Warner (D-Va.), who chairs the Senate Intelligence Committee, warned in a CBS News interview on Sunday.

Many senators share concerns about TikTok and its influence on Americans, but members on both sides of the aisle expressed unease about the House legislation on Tuesday. They cited how the bill takes specific aim at one company instead of the industry at large, which could open it up to potential legal challenges. They also worried about its effects on free speech in the U.S. and whether there might be unforeseen consequences to U.S. businesses.

“What are the unintended consequences of this targeted approach to future companies?” asked Sen. Thom Tillis (R-N.C.). “And what about some of the European parliaments who may have issues with some of our platforms? So, I think we just need to be careful.”

Sen. Elizabeth Warren (D-Mass.) suggested instead the Senate look at legislation she authored alongside Sen. Lindsey Graham (R-S.C.) last year that would establish an independent commission to help regulate online platforms to help protect consumers and their privacy.

“We need curbs on social media. But we need those curbs to apply across the board,” Warren said when asked about the House TikTok bill.

“We don’t want TikTok to be used by the Communist Party to influence our elections, right?” added Graham. “Having said that hundreds of millions of people like the website, is there a way to keep the website up?”

There are several other proposals in the Senate intending to curb the harmful effects of social media companies, like the American Innovation and Choice Online Act and the Kids Online Safety Act, but none have received a floor vote in the upper chamber.

Sen. Josh Hawley (R-Mo.), a vocal critic of TikTok, complained in a post on X, formerly Twitter: “They should just go ahead and put a sign on the Senate doors: ‘Owned by Big Tech.’”

Sen. Rand Paul (R-Ky.), meanwhile, reiterated his opposition to efforts to ban TikTok over free speech grounds, an argument representatives for the viral app have made as well.

“180 million Americans use this company and if you ban the ownership of it, and it goes out of business, you’re taking away their right to express themselves as well,” Paul told reporters on Tuesday.

The House bill does not ban TikTok outright. It would block the viral app in about six months if its parent company fails to divest it. House leaders are fast-tracking the bill’s passage on what is called a “suspension” calendar, meaning they will need two-thirds of votes in the chamber to pass it.

Congressional offices were flooded with calls in recent days after the company sent pop-up messages urging users to call lawmakers’ offices in protest, many of them young teens.

Last week, former President Donald Trump raised concerns with banning TikTok because, he said, that would only help Meta, the parent company of Facebook. In 2020, when he was president, however, Trump threatened to ban the app himself over similar national security grounds.

Trump’s comments didn’t appear to alter the positions of Republican senators who have endorsed his 2024 presidential bid on Tuesday.

“I think that we need to also look at Meta and the others ― Google. They’re all in a position to manipulate and addict Americans,” Sen. Cynthia Lummis (R-Wyo.) said. “TikTok is the most notorious with the relationship of the Chinese Communist Party. We need to look at all of them.”

Meanwhile, Sen. John Fetterman (D-Pa.), who also supports reining in TikTok, suggested Trump reversed his position on the matter because he is benefiting financially from it. For example, Trump recently hosted GOP megadonor Jeff Yass, who is a billionaire investor in ByteDance, at his Mar-a-Lago club and sought his support in the presidential race. Former Trump adviser Kellyane Conway is also reportedly lobbying against banning TikTok.

“My question is, what do they have on Trump?” asked Fetterman. “I don’t get it. That used to be a banger ― politically bipartisan. Now watch how quickly are they going to fold like a cheap card table, just like on Ukraine.”