If my federal tax return hasn't come in time from the expected date, what should I do?

All you can do now is, wait. At least you know that the IRS has your filing. It does not matter who sent your 1040 to the IRS. The IRS is the sole destination for tax returns. No one has discovered a way to make the IRS speed up sending out refunds. No one ever will because the IRS is an overwhelmed, over worked, under funded and under staffed government bureaucracy. Eventually you will get the pay off of your no interest loan to the government.

Have you thought of paying just enough by estimates or withholding to avoid a penalty and let the government wait for your check?

You should continue to wait. There is no "expected" date for a tax refund. TurboTax may have shown you an estimated date that is 21 days after you filed. But that's just an average, not a schedule or a guarantee. It's not based on any actual information about your tax return.