This is probably a good reason to leave enough in your checking accounts to cover bills that may come up. You may not always be able to transfer money from your online savings account as fast as you expect.
This may also be a good reason to go with a high-yield money market account (which has limited check writing capabilities) over a high-yield savings account like EmigrantDirect. The other possibility would be to open a checking account at the same bank that has the high-yield savings account. This can be done at banks like HSBC and Presidential. Internal transfers usually can be done with no delays.