What they are not willing to do is support a GOP politician
Irrelevant to the issue at hand: I never suggested supporting a GOP politician.
I suggested an apolitical outsider: someone other than a congressman. A person untainted by political aspirations. I suggested a Medal of Honor recipient, but we could go with an astronaut, or the head of a major charitable organization, or someone else with an awe-inspiring origin story who hasn't yet managed to piss off half the country.
That's why Democrats have, in fact, already indicated that they are willing to support a bipartisan GOP Speaker who will make a deal with Democrats to help achieve some of those goals.
They've asked the GOP to nominate someone the Democrats can support. That's the wrong approach. Anybody the GOP nominates will automatically be considered a partisan hack by many of the Democrats. Any division in the Democratic ranks would be very damaging. Democratic leaders would have an extremely difficult time trying to wrangle all Democrats to support any candidate the GOP puts forward.
We want the opposite. We want 212 Democrats voting for this person. That means we have to nominate this person.
This person's unassailable record needs to scare the GOP leadership into believing 6 or more of their own members may defect. An MoH recipient can do that.
As soon as they believe that, GOP leadership has to jump on the bandwagon and back this person as well.
It would be incredibly damaging to the GOP for all of their members to shun an MoH recipient. Current and former military would crucify them.