Senate Majority Leader Harry ReidHarry Mason ReidMcConnell not yet ready to change rules for Trump nominees The Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Trump to press GOP on changing Senate rules 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. Charles SchumerCharles (Chuck) Ellis SchumerThe Hill's 12:30 Report — Sponsored by Delta Air Lines — GOP centrists in striking distance of immigration vote Schumer: Trump should take Kim Jong Un off 'trip coin' Overnight Finance: Trump signs repeal of auto-loan policy | Justices uphold contracts that bar employee class-action suits | US, China trade war 'on hold' 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.