It depends upon the terms of their cash-back offer.  Did it stipulate that the DD must be maintained for a certain period of time, or simply that it be established?

Here is what it said

Terms and Conditions:

Bonus/Account Information: Offer not available to existing Chase checking customers, fiduciary accounts and those who have closed an account within 90 days. Offer valid through 10/6/12. To receive the bonus: 1) open a new Chase Total CheckingSM account, which is subject to approval; 2) deposit $100 or more within 60 days of account opening; Your opening deposit cannot be money held by Chase or its affiliates, nor can the bonus be used as the opening deposit. You can only receive one checking account-related bonus per calendar year. If your checking account is closed within six months, we will deduct the bonus amount at closing. Also, if your account is closed within 90 days, an Account Closing Fee of $25 will apply.

You can probably switch your DD to US Bank, but you will need to keep your Chase account open for at least 6 months.  And, your Chase account may have monthly fees that are waived with direct deposit of a certain amount.  You need to read your account terms to determine what is needed to offset the monthly maint fees.

If your direct deposit is coming from employment, you may be able to set up a second direct deposit so that you can simultaneously have direct deposit going into both Chase and US Bank.  This is possible with many employers these days, you just have to inquire about it.  Where I work, we can have up to 5 separate bank accounts for direct deposit.  One account is for "net pay" and the other four bank accounts have to be flat dollar amounts per paycheck.

Congrats on those $200 bonuses!!  I'm jealous!

FICOs: Walmart TU08 800 5/13/13; TU98 783 5/2/13; EQ 758 5/2/13; EX 741 (per US Bank 7/24/12)

My Wallet: Amex Gold NPSL w/Pay-Over-Time; Amex Optima Platinum $25K; Amex Costco TE $5K; Amex BCE $12K; BofA Visa $10.1K; Cap1 Cash Rewards Visa Signature $8K; Chase Freedom MC $7.5K; Citi Simplicity Visa $11.9K; Discover $5K; US Bank Cash+ Visa Signature $20K; Walmart Discover $10K

The $200 bonus is only available to customers who received a special mailing from US Bank. There is a code floating around from ratenerd or some site like that but I called US Bank and they will not honor it if you are not on their customer list who received the mailing. Just an FYI before you waste 6 months of banking thinking there is a bonus coming your way. Unless, of course, you actualy received the mailing.

And yes, you would need the DD to come from your employer, not from your chase bank account.