You can file an amended return with TurboTax, but it's not clear that you will need to file an amended return. After the law is passed and signed, the IRS will issue guidance about what to do if you already filed and making part of your unemployment tax-free would increase your refund or reduce your tax. Wait until the IRS has issued the instructions before you do anything.
You will not get a new 1099-G. The 1099-G reports the full amount of unemployment benefits that were paid to you, whether or not it is all taxable. The 1099-G does not show how much of it is taxable or not taxable. Any adjustment of the taxable amount will be made on your federal tax return, or on an amended federal tax return, or by the IRS.
