The transaction limit is CURRENTLY limited to 7tps.  This can be raised with a hard fork.  I don't want to trivialize it (as some do) but I find it hard to believe this limit will last forever.  I mean imagine if in 1970s someone had said CPU will never break the 1Ghz barrier or 1TB of storage will never exist, or nobody will need more than 640KB of RAM.  It would seem logical in the short term but almost idiotic in the long term.

Eventually the 7tps "limit" will constrain future growth of Bitcoin and as such there will be increased pressure by stakeholders (users, bitcoin related companies, developers, miners, merchants, etc) to raise the limit.  While miners don't want to see unlimited tx volume (as that means no fee pricing power) they also don't want to see Bitcoin die.  With ASICs they can't simply switch to LTC so they have a very vested interest in ensuring Bitcoin adapts.

My guess is either Bitcoin dies out or the limit is eventually raised.  Either way that means the 7tps is a non-issue.  We will solve it or Bitcoin will by default ( 0 tps < 7 tps).

As for how can off chain tx work.  Currently you can pay someone on MtGox or someone on coinbase with off chain tx.  Either entity simply updates a ledger.  If Mtgox (clients) have a combined sum of 1,000,000 BTC and you transfer 1 BTC from your account to another MtGox account holder then MtGox clients still have a combined sum of 1,000,000 BTC.  There is no need to EVER record a block chain tx.

However today this is limited to a single entity.  It only works if you and your receiver are both on MtGox.  However look forward a couple years and say you have a MtGox account and someone else has a coinbase tx.  In theory MtGox and Coinbase could extend reciprocal lines of credit so MtGox notifies coinbase and coinbase instantly reflects your new balance.  Once a day MtGox and coinbase "settle" the books with a single blockchain tx.  Just to be clear this does NOT currently exist but it could.  Eventually a network of these entities could exist.  In someways this resembles a banking network with one SIGNIFICANT difference.  Today you can't be your own fiat bank (well at least not with any reasonable cost) but you can choose to be your own Bitcoin bank.  All you need the ability to run a full node and willingness to put all tx on the blockchain.

Disclaimer:  hopefully that made sense.  I broke open a bottle of port, LBV 2005 so while the above made sense I can't guarantee it will make sense to anyone else.