WASHINGTON ― A growing number of Democrats are pledging to block the consideration of all other legislation on the Senate floor until Republicans allow a vote on appropriations bills passed by the House last week.

The hardball tactic aims to put added pressure on Senate Majority Leader Mitch McConnell (R-Ky.) as the partial federal government shutdown enters its third week. He has said that he will not allow a vote on the spending bills because they would not receive a signature from President Donald Trump, who is demanding that Democrats agree to fund construction of a wall on the U.S.-Mexico border.

Sen. Chris Van Hollen (D-Md.), who represents a state with a large number of federal employees, urged Senate Democrats to adopt the strategy in a tweet over the weekend. Since then, it has been endorsed by several progressive groups and nearly a dozen of his Democratic colleagues in the Senate.

Senate Democrats should block consideration of any bills unrelated to opening the government until Sen. Mitch McConnell and Senate Republicans allow a vote on the bipartisan bills the House passed to open the government. Mitch, don’t delay. Let’s vote! — Chris Van Hollen (@ChrisVanHollen) January 5, 2019

He will need nearly all Democrats on board, however, in order to prevent Republicans from clearing the chamber’s 60-vote threshold to bring a measure to the floor.

The first test will come Tuesday afternoon, when the Senate is scheduled to vote on a motion to proceed to open debate on a Republican Middle East policy package that includes Syria sanctions and a measure that aims to block boycotts of Israel. The latter has been endorsed by some Democrats, but critics say it violates the First Amendment right to free speech.

A senior Senate Democratic aide said Monday that Minority Leader Chuck Schumer (D-N.Y.) would join the opposition to taking up the foreign policy legislation, known as S.1, before the Senate votes on the House-passed spending bills.

“Senate Republicans should instead bring to the floor the House-passed bills to reopen the government,” the aide said Monday.

Schumer is a prominent ally of Israel in the Senate, and he has backed similar measures that would have made it a felony for Americans to support the international boycott, divestment and sanctions movement against Israel.

Sen. Marco Rubio (R-Fla.), an author of the anti-boycott bill, argued that the shutdown is not really the reason Democrats are coming out against the foreign policy package.

“A huge argument broke out at Senate Dem meeting last week over BDS. A significant # of Senate Democrats now support # BDS & Dem leaders want to avoid a floor vote that reveals that,” Rubio tweeted Monday.

But Sen. Chris Murphy (D-Conn.), who serves with Rubio on the Senate Foreign Relations Committee, disputed that characterization in a tweet of his own.

“You know it isn’t true that ‘a significant # of Senate Dems support BDS’. Really dangerous to play politics w support for Israel,” Murphy tweeted.

It’s unclear whether Democrats can remain united in blocking all legislation from coming to the floor. A public lands bill that was held over from the last Congress is expected to get a vote next week, for example ― and it has support from a number of Western Democratic senators.

For now, though, the tactic seems to be Democrats’ best hand before Trump’s national address and trip to the border later this week.

“Senate Republicans should not treat this legislative work period like it’s a time to catch up on miscellaneous items. People are suffering, let’s vote to fix it,” Sen. Brian Schatz (D-Hawaii) tweeted on Monday.