Bluntly, McConnell is the most unpopular Senator today. In Kentucky, he's at 34%. He's up for re-election in 2020 but has high unfavorables. He wants this behind him to start fund raising. The longer the Speaker withholds the bill, the worse it is for the Senators in Alabama, Alaska, Arkansas, Colorado, Delaware, Georgia, Idaho, Illinois, Iowa, Kansas, Kentucky, Louisiana, Maine, Massachusetts, Michigan, Minnesota, Mississippi, Montana, Nebraska, New Hampshire, New Jersey, New Mexico, North Carolina, Oklahoma, Oregon, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Virginia, West Virginia, and Wyoming.
There are three Senate Classes. Classes I and II have 33 senators, Class 3 has 34 senators and they're up in 2022. There are twice as many republicans up for re-election in 2020 as Democrats.
Republicans Alexander, Lamar (R-TN) Capito, Shelley Moore (R-WV) Cassidy, Bill (R-LA) Collins, Susan M. (R-ME) Cornyn, John (R-TX) Cotton, Tom (R-AR) Daines, Steve (R-MT) Enzi, Michael B. (R-WY) Ernst, Joni (R-IA) Gardner, Cory (R-CO) Graham, Lindsey (R-SC) Hyde-Smith, Cindy (R-MS) Inhofe, James M. (R-OK) McConnell, Mitch (R-KY) Perdue, David (R-GA) Risch, James E. (R-ID) Roberts, Pat (R-KS) Rounds, Mike (R-SD) Sasse, Ben (R-NE) Sullivan, Dan (R-AK) Tillis, Thom (R-NC)
Democrats need to win 4 seats to retake the Senate. The most vulnerable republicans are Cory Gardner (CO), Susan Collins (ME), Thom Tillis (NC), Martha McSally (AZ), Gary Peters (MI), Doug Jones (AL), Joni Ernst (IA), Jeanne Shaheen (NH), John Cornyn (TX). The republicans will likely pick up Dough Jones's seat in Alabama, unless another Klansman runs against him.
There's no particularly urgency for the Speaker to forward the bill. She can hold it. It should expire at the end of this Congress but there are votes to hold the same impeachment vote in the next congress in January, if need be. She can announce the bill will be withheld until the Supreme Court rules on the questions of executive privilege and evidence subpoeaned by the House committees.