It would be completely unprecedented in the US, but if they dems aren't actively trying to peel off 5 moderate Republicans for a caretaker government they are doing themselves a disservice.
Then again, there is a distinct likelihood this is all theater and Jordan will gain votes and the pressure campaign will work to flip enough people to get in on subsequent votes today, remember McCarthy had to do 15 votes.
If Jordan doesn't wrap this thing up today though, then Dems should be pouring money in to target the Biden district/swing district R's and offering up a bland agenda of continued funding of government and a "seat at the table" as well as committee chairs and leadership positions to the Republicans who join the unity government.
I don't see 5 Republicans taking that bait, but getting crushed from both sides with the alternative being Manchin/Sinema level veto power would be a tough spot to put those little R weirdos in.