My fiancee and I have set a date for our wedding over a year from now, so we're planning to send out save the date cards. Can we ask for tentative RSVPs now to save ourselves the hassle of first- and second-round invitations later?
Are you really saving the date?
Save the date cards provide your family and friends with information; invitations request information from them. Trying to combine the two would, I suspect, be confusing for your guests and probably wouldn't get you accurate enough information this far in advance to be useful.
However, there are lots of less structured ways that you can gauge whether or not people plan to attend. The best of these options is to start talking to your friends and family about the wedding now. In conversation, inevitably it will come up that some of these people already know they're unavailable. Encourage your parents to start talking to their portions of the guest list with an ear towards this sort of information, too. Now would be a good time to set up a wedding website (and put the address on the save the date cards). Often, people will indicate on the guest book page that they're sorry they won't be able to celebrate with you in person.
If you do find out through one of these means that someone is unavailable, then you have to decide whether to send them an invitation. Sending one when you know the person is unavailable could be seen as fishing for gifts, but not sending one could be seen as a snub. If you don't know someone's plans in advance, you can't be expected to contend with that set of social conventions.
You could also decide to forgo the save the dates and just send out the actual invitations a bit earlier than you would otherwise - say, six months before the big day instead of the typical six weeks. There are two advantages to that approach: 1) You have more time to deal with the second round invites, and 2) If you're hoping to keep things small, more of your invites will be busy if you don't give them a year's notice.
It's worth pointing out that even when people do RSVP that they'll be there, some guests inevitably turn out to be no-shows. It's frustrating and disappointing, but I don't know of a single wedding where that hasn't happened with at least one guest. It's less common for someone who RSVPed no to show up anyway, but I have heard of that, too.
Mazel tov to both of you, and good luck with the planning!