What's amusing is they seem split about why they're saying they'll challenge many Elector votes; some, like Rep. Sheila Jackson Lee (D-Texas), claim:
...that she and her allies plan to challenge the validity of electoral votes in multiple states, where she argued voter suppression tactics may have tainted the outcome. She said a separate batch of challenges will focus on disqualifying electors who may have been ineligible to serve at all.
"This is an American question of justice and fairness and the appropriate running of presidential elections," Jackson said
...the House Democrats' protest “is not about trying to stop Donald Trump from becoming President,” but “the fact that our liberty, freedom and democracy were compromised by Russia’s intrusion into America’s election."
All of the 538 Elector votes can be challenged at will by these House Democrats, but they must do so in writing and convince a Senator to also do so in writing for any challenge to go any further. If that criteria is met, then the House and Senate split up to debate the challenge separately (max debate time is 2 hours, with 5 minutes max allocated for each debater).
Feasibly, then, 538 challenges debated for the 2 hours max could take up 1,076 hours, or forty-five 24-hour days, which would take us to February 20th. But the Dems aren't going to challenge any Hillary votes, so challenging Trump's 304 debated for the max would consume 25 days, which takes us to January 31st.
After the House and Senate separately debate all challenges, they reconvene in Joint Session to announce the results of those debates, and then Congress must simple majority vote to agree to reject each and every challenged Elector vote put forth from the debates. The political Party makeup of the 115th Congress is 293 Republicans, 240 Democrats, and 2 Independents (the other 3 of the 538 are the Elector votes from the District of Columbia, which has no Representatives or Senators).
The result of all that effort? Any Elector vote Congress votes to reject is simply not counted, so 35 Elector votes for Trump need to be rejected by the majority Republican Congress for any different result from present President-elect Trump reality to occur.
What odds would you offer on that actually happening?
Figurative last call for Democrats for at least the next two years begins at 1:00pm EST today; let's see how ugly they get before the lights go out.