I wouldn't have much faith in any pledge that a politician made before the election. If such Democrats were voted out of office, they might feel freed to vote along with the party and their own liberal predilections.
Phil Kerpen over at NRO has a better idea of how to block such legislation. He points out that there are now six unelected senators in the Senate whose positions will be filled in November before the lame-duck session. Five of those states have laws that indicate that whoever wins the Senate race could be sworn in and seated right after the election instead of waiting until January 3. The Republicans have the opportunity to pick up seats in Delaware, Colorado, and Illinois. Who knows what will happen with West Virginia's seat. The Republicans should press for the winners of those elections to fill the terms of these unelected senators immediately after the November election.
Colorado and Florida, like Illinois, are holding elections for full six-year Senate terms to replace their appointed senators — and their laws are silent on the date the new senators should be seated. Given the ambiguity, state officials appear inclined to allow appointed senators to remain through the end of the year. The Congressional Research Service has, however, suggested a way to immediately respect the will of the voters, noting that “it is often customary for the interim senator to resign his or her seat immediately after the election, and for the governor to appoint the special-election winner to serve the balance of the term.” Appointed senators George LeMieux of Florida and Michael Bennet of Colorado (if he loses his election bid) should respect this custom.Of course, the Democrats would oppose such a step that would dilute their majority in the Senate, but they'll have a hard time arguing that an appointed senator should take precedent over a duly elected senator. Do they really want to stand against the people's choice so that the Democrats can try to push through bills that are so unpopular that they didn't dare bring them up before the election? I wouldn't put such actions past these Democrats, but the state legislators and governors who might want to run again may not be so willing to be so indifferent to how their constituents voted.