As per the Milwaukee Journal Sentinel:
Perhaps the most important deadline is Dec. 19, when electors around the country must meet to cast their Electoral College votes, said Edward Foley, an expert in election law at Moritz College of Law at Ohio State University.
"That is a hard deadline and if a state were to miss that deadline, it would be technically in jeopardy of not having its electoral votes counted," he said.
The deadline for completing a recount is thirty-five days after the election, which is December 13th this year. The electors actually vote six days later, on the 19th. If they don't send the electoral college votes on that day, then Congress isn't required to accept the electoral votes from that state.
Of course, it is a Republican Congress and Wisconsin went for the Republican candidate, so they might offer more leeway than they would for a candidate from another party.
If all three recount states fail to send in their electoral college votes by the deadline, it is possible that there won't be enough electoral votes to make a majority. If neither candidate gets 270 votes, the election goes to Congress with the top three vote getters in the electoral college. Absent any faithless electors, that would be Donald Trump and Hillary Clinton.
With a single faithless elector refusing to vote for Trump, Michigan (16 electoral votes) and Pennsylvania (20) failing to submit electoral votes would leave Trump with 269 electoral college votes. With seven, Wisconsin (10) and Pennsylvania would be sufficient. With eleven, Wisconsin and Michigan. And faithless electors would allow a third candidate to be considered, perhaps someone that could get Republican votes in Congress.
Recounts taking too long makes the unlikely prospect of faithless electors more feasible. It would currently take 37 to throw the election to Congress. Or if the 232 Clinton electors join with 38 or more Trump electors, they could pick a compromise candidate. However, the only time that that many faithless electors existed, it was because their candidate died. Other than that, the next largest numbers of faithless electors were for the vice-presidential candidates. But if one or more Trump states fails to vote at all, fewer faithless electors are required to throw it to Congress.
In Congress, if the third option were to be more palatable to select Republicans, they could join with Democrats to choose that person. Of course, Trump would still have the inside path. There are so few states where the Democrats are even close to having enough votes to flip the state. Their large leads in California and New York are wasted in a vote by states.
Note that this is all really unlikely. The states will almost certainly all finish their recounts on time and only a scattered few electors will be faithless. Even if the vote did go to Congress, the House would almost certainly pick Trump. Particularly with people like DeVos and Priebus part of the administration.