$2 billion won't buy jack shit in the way of R&D on a problem like this.
For it to be entirely efficient there has to be market incentives... such as having a clear economic outcome with manageable risk.
Otherwise it will mostly just be throwing money at it with hopes that something will come of it. Something the government is always more than willing to do. But more capital efficient channels... not so much
2) Transport and energy are areas where the low-hanging fruit has already been harvested. Incremental improvements are enormously expensive in such areas.
To put the $2 billion figure into context, Intel spends $6-10 billion a year on R&D, most of which goes to fab/semiconductor research. That's what it costs to do the research just to go from 32 nm to 28 nm to 22 nm, etc, every 18 months. This is because semi-conductor research is frighteningly expensive, and is also an area where the low hanging fruit has already been harvested.
Making fundamental breakthroughs in energy and transport isn't a $2 billion research project. It's probably not even a $20 billion research project (the cost of the Manhattan Project). It might be a $200 billion research project (the cost of the Apollo Program).
There is a lot of low hanging fruit in simply applying well known techniques. For example, Toyota has made big advances by simply removing excess metal from their engines. GM could have beat them to it in the 1960s by hiring a few interns.
There is also a great deal of efficiency to be gained by insulating buildings. A comprehensive approach to automating insulation retrofits would give tremendous savings but would not take more than $50M or so for the engineering.