Senate Majority Leader Harry ReidHarry ReidThe Memo: Trump pulls off a stone-cold stunner The Memo: Ending DACA a risky move for Trump Manchin pressed from both sides in reelection fight MORE (D-Nev.) filed for cloture Thursday to force a vote on the so-called Buffett Rule, which would raise taxes on those making more than $1 million annually. 

A Senate leadership aide told The Hill that Reid plans to vote on the rule on April 16. 

Sen. Chuck SchumerCharles (Chuck) Ellis SchumerSenate Dems hold floor talk-a-thon against latest ObamaCare repeal bill This week: Senate wrapping up defense bill after amendment fight Cuomo warns Dems against cutting DACA deal with Trump MORE (N.Y.), the Senate's top messaging Democrat, said on Sunday that Democrats planned to debate the legislation in mid-April.

Named after billionaire Warren Buffett, a backer of President Obama, the rule would require Americans making more than $1million annually to pay a minimum income tax rate of 30 percent.

Obama has been a strong advocate of the bill as part of his aim to ensure. The president has said many times that taxes on the wealthy should be raised so "that we don't have billionaires paying a lower tax rate than their secretaries."

Even if the Buffett Rule successfully moves through the Democrat-controlled Senate, it's likely to die in the GOP-controlled House.