Senate Majority Leader Harry Reid (D-Nev.) late Thursday night filed cloture on the Disclose Act, which aims to blunt the impact of a Supreme Court ruling lifting restrictions on corporate and union spending on political advertisements. The vote could come as early as Tuesday.

Reid is bringing up the campaign-finance bill even though he has yet to secure the votes needed to break an expected Republican filibuster.

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Democrats and watchdog groups point to polls showing that a majority of the public disapproves of the high court’s decision. Reid and others will no doubt use the issue for campaign ads in the fall regardless of whether the legislation moves forward.

The legislation Reid is bringing to the floor has been modified by Sen. Charles Schumer Chuck SchumerFirst woman sentenced for her role in Nxivm sex cult Ocasio-Cortez calls Trump a 'white supremacist' after debate Democrats rip Trump for not condemning white supremacists, Proud Boys at debate MORE (D-N.Y.) in an attempt to win the support of centrist Maine GOP Sens. Olympia Snowe and Susan Collins, who have both supported restrictions on campaign finance in the past.

Schumer has stripped and changed some provisions in the House-passed version of the Disclose Act that Collins and conservative groups have criticized as creating an unfair political advantage for unions over corporations.

But those changes are jeopardizing union support for the legislation.

“Based on reports, we are concerned that recent developments could hamper working families’ ability to have a voice in the political process,” an AFL-CIO spokesman said of the modified bill. “We continue to review the legislation and fight to ensure that the final bill addresses the tilted advantage that big business has enjoyed for far too long.”

Rankling labor organizations, however, could play to the Democrats’ advantage and help them court Snowe, Collins and some conservative Democrats wary of the House bill’s exemptions for unions and other special interests.