Elon will not wait for Congress. Who will pay for it?
1. The people who want to move there - target price $500k USD.
$500,000 is the estimated price at which the demand is estimated at 80,000 tickets. Elon figures that if the price of moving to Mars is comparable to buying a home in California, the number of people who could afford to go and would want to go is ~80,000. So that's ~$40B or so.
2. Elon - maybe worth $50-100B by then?
If we assume that SolarCity and Tesla will continue to grow for the next 10-20 years, then Elon's net worth will probably be ~$50B or so. Not enough to fund a full Mars colony, but it'd be a really good start.
3. Satellite internet profits
The recently announced satellite internet effort by SpaceX, financed by Google and Fidelity, is intended to provide high-speed, low-latency global internet access to billions of people. Elon expects to be able to fund part of the Mars colonization project with profits from that.
4. NASA / Congress
NASA already expects to spend many billions on making trips to Mars. It does not seem unlikely that, in 20 years, they would be willing to join some efforts and allocate $10-30B towards Mars colonization with SpaceX.
5. VCs and billionaires.
The Martian economy may have a rough start but will probably grow wildly once established. SpaceX already attracts VC funds in the billions from large firms and billionaires, and this will certainly be amplified in the future.