If there is enough to implement it with a big tax increase but not without a big tax increase, and if that makes it infeasible ... isn't that exactly an ideological problem?
(For the avoidance of doubt, an ideological problem can be a serious real problem. If a basic income can't be implemented without a tax increase that voters would never tolerate, that's a good reason not to do it. If it can't be implemented without a tax increase that would wreck the economy, that's also a good reason not to do it, but I think that would rightly be called a numbers problem rather than an ideological one.)
(For the avoidance of doubt, an ideological problem can be a serious real problem. If a basic income can't be implemented without a tax increase that voters would never tolerate, that's a good reason not to do it. If it can't be implemented without a tax increase that would wreck the economy, that's also a good reason not to do it, but I think that would rightly be called a numbers problem rather than an ideological one.)