Today the Bitcoin network is restricted to a sustained rate of 7 tps by some artificial limits. These were put in place to stop people from ballooning the size of the block chain before the network and community was ready for it. Once those limits are lifted, the maximum transaction rate will go up significantly.
Of course, a significant increase from 7tps still might fall well short of what is required for real commerce. If you look at this graph of the daily transaction rate, you can see that the actual performance of the network is somewhat less than 1tps:
