The Senate will take two votes on Thursday on Democratic and the Republican plans, both of which are expected to fail to get enough support.
Tax hikes are backed by the AFL-CIO, which suggests in the letter raising additional tax revenue from Wall Street and the richest 2 percent of taxpayers.
"Replacing sequestration with progressive tax revenue would minimize harm to the economy because the kind of spending subject to sequestration has far more 'bang for the buck' than tax breaks for millionaires," Samuel wrote.
The AFL-CIO letter outlines that the Republican bill "would inflict just as much harm on the economy as sequestration."
The across-the-board cuts will go into effect on Friday, ahead of a White House meeting between President Obama and congressional leaders.
Obama said Thursday that he wants leaders to "be ready to talk solutions."
Another reason why the union is pushing for a repeal rather than replacement "is because Republicans are using it as bargaining leverage to demand Social Security, Medicaid and Medicare benefit cuts," Samuel wrote.
"These demands are wildly unpopular, which is why Republican leaders keep manufacturing crises to get their way," Samuel wrote.
The Congressional Budget Office estimate that the cuts would cost 750,000 jobs this year.