They are different animals.
Nuclear provides approximately 20% of the nations electricity
Petroleum provides approximately 3% of the nations electricity (2005)
Nuclear, along with Coal, is a base load type plant (24 hour generation).
Petroleum is a peak plant (when demands are higher).
With overall energy usage (not just electricity), nuclear is about 9% while petroleum represents about 40% of total US Energy Consumption.
So where is petroleum consumed in the US? By Sector...
68% Transportation
25% Industry
4% Residential
2% Commercial
1% Electricity Production
As you can see, increasing Nuclear won't do much to solve our dependency on Petroleum, unless we increase Nuclear Transportation. While nuclear powered submarines and shipping vessels do exist, land based transportation won't likely be developed.
Hybrid and Electric vehicles are currently the best option at reducing petroleum consumption. However, personal economics come into play and most people would rather spend less on a gas guzzler and complain at the pump than spend more now for a hybrid or electric vehicle. The costs of these vehicles will continue to lower over time. One should also not count out alternatives (increased public transportation).
As for nuclear...
Why not increase nuclear? There are many people who are both for and against nuclear and the regulative body, the Nuclear Regulatory Commission (NRC), is caught in the middle of them. The NRC sets the guidelines and based on those guidelines, a utility can or cannot operate their nuclear reactor. It is responsible for approving new reactors and renewing the operating life of existing reactors.
The nuclear industry is serious about mitigating risks and preventing negative consequences. Like any action we take, however, there are risks associated that cannot fully be prevented. Every commercial nuclear disaster can and have taught the nuclear industry to further prevent human error and equipment failure. The Institute of Nuclear Power Operations (INPO) was created after Three Mile Island to improve the safety and standards of commercial nuclear power. It is not a government agency. Many times, the guidelines set by INPO are higher than those set by the NRC.
The lessons are still to be learned from Fukushima and they will be incorporated into commercial nuclear power operation. Public perception will sway one way or another, but overall the benefits and risks must be weighed. As long as it remains profitable, private companies will invest in it.
The future of nuclear power does require solutions though. Of prime importance is spent fuel storage. Congress had agreed to find the solution to this problem with the 1982 Nuclear Waste Policy Act. The nuclear industry has put billions of dollars (taxed from each kW-h sold) into a fund dedicated to this solution. Congress has yet to solve this issue and are further from a solution after the canceling of a deep geological storage facility at Yucca Mountain. With the canceling of that project, a Blue Ribbon Panel had been formed to propose solutions to spent fuel handling.
Another step is the approval new reactors. It is believed that once the AP1000 is approved by the NRC for one proposed site, many others will follow. Although new reactors have more inherent safety features designed, the risks will still be there.
The economics of uranium fuel will eventually come into play (not likely before fossil fuels), which will cause us to develop collection technology, revisit reprocessing legislation, or redesign reactors for thorium fuel.
Those interested in carbon emission reduction should be big proponents of nuclear (as the other major base load plant is coal). The amount of coal vs nuclear fuel for the same energy equivalence is astounding. However, many see the after effects of nuclear as worse than coal burning.
Personally, I think all energy technologies should work towards our energy issues and allow the market costs determine what is viable or not. Technology improvements and manufacturing cost reduction are needed in Solar to get to grid parity, but it shouldn't be at the expense (or elimination) of either nuclear or coal. Each technology has it's pros and cons.