Tell your client about Constant Contact. They are going to handle this much better than you ever could. It's also cheaper than your time.
In the event that fails you have a couple options.
If they already have an email server, leverage that to do the email broadcasting. In other words, relay the mail through that server.
If you can't do that, go download a free email server. I've been using hMailserver. Set it up and relay through it.
If you can't do that, write your own SMTP processing engine. Don't attempt to send the emails directly from ASP.Net. Queue them up in a database and write a windows service to handle the mail broadcasting.
Sending emails can sometimes take several seconds per email. This could completely hose your website while it's trying to handle sending 1000 emails.
A number of mail servers are configured with grey listing, meaning that they require you to send the same email twice in order to prove you aren't a spammer.
Next, getting the DNS appropriately set up can be a PITA. Which is why I suggest constant contact. I have one client that took nearly 5 years to finally get their DNS configured; and yes, I gave them explicit instructions once a year on what to do. Reverse DNS is critical.
Another thing is that some recipient servers have a limit on the number of threads they will accept from you at once. Most mail servers are built to take this into consideration. If you cross that boundary, then the recipient servers will consider you a spammer and take appropriate action.
Another problem area is in sending to a bad address, over and over again. AOL and others will consider you a spammer just for this one thing.
Point is, you really don't want to write this yourself.