Final answer:
President Obama is referring to the Supreme Court case Citizens United v. Federal Election Commission in his 2010 State of the Union address, which allowed corporations, including foreign corporations, to make unlimited campaign expenditures. This decision has been widely criticized for giving special interests too much influence in elections.
Step-by-step explanation:
The Supreme Court case that President Obama referred to in his 2010 State of the Union address is Citizens United v. Federal Election Commission. In this case, the Supreme Court ruled that corporations have a First Amendment right to make unlimited expenditures in candidate elections, including foreign corporations. The decision opened the door for a substantial increase in campaign spending by special interests, which President Obama criticized as a threat to the American people's ability to decide elections.