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Senate Majority Leader Harry ReidHarry ReidDems face identity crisis Heller under siege, even before healthcare Charles Koch thanks Harry Reid for helping his book sales MORE (D-Nev.) also announced Tuesday night that his chamber would vote on a motion to proceed on the 21st Century Postal Service Act (S. 1789) on Thursday. On Tuesday, Reid said he would "fill the tree," or stack the process with his own amendments to prevent others from being considered, on the legislation after Sen. Rand PaulRand PaulRand Paul pitches ObamaCare repeal wish list Paul: 'Weak-kneed' GOP colleagues 'need to get over themselves' New Alexandra Pelosi documentary brings together GOP, Dem members MORE (R-Ky.) announced his intention to attach an amendment cutting U.S. funding to Egypt.

Sen. Joe Lieberman (I-Conn.), one of the cosponsors of the bill, also signaled on Tuesday that he hoped to find some kind of compromise between Republicans and Democrats over possible additional amendments.