Try to build a few high-potential relationships rather than exchange your card with everyone.
The best way to do this is by showing interest in the people you meet instead of trying to sell yourself at every turn. You can offer to provide information that's useful to them later, either at the conference or by connecting with them down the road. In the meantime, make your conversations about them, not about you. Don't offer your business card until you've established a relationship.
A little sincerity goes a long way towards relationship-building.