You are among millions who have now been affected by a mid-tax season change in the tax law. Patience will be necessary.
TurboTax will update the software for the unemployment but there is no timeline yet.
It can take weeks to several months or more for the changes to be made to tax software. First the IRS has to change its forms. The tax software has to be changed; the IRS has to test and approve of the software. Do not expect changes in the software to happen quickly. TurboTax may have more information in the near future AFTER the bill is signed into law, and some more details emerge about how Congress and the IRS will implement the changes.
TurboTax will do whatever the IRS tells it to do. The IRS has not released any announcements yet, and it would usually take a couple of weeks for TurboTax to incorporate any official changes. If you have not filed, it is probably a good idea to wait until you get more instructions. I think it will be easier to file one correct return even if you have to wait, then to file now and then have to file an amended return to claim a refund of the overpayment.