Since you asked, several, if not most, states allow the iniative (citizen-proposed laws) or referendum (citizen approval/disapproval of laws passed by the legislature). These were part of the “Wisconsin Plan” of reforms started 100 years ago. They never were incorporated into the Federal system, so to answer your question, no we can’t vote out ObamaCare.
As to their constitutionality, if a Federal judge doesn’t like what the voters want, like say same-sex “marriage”, then of course it is unconstitutional.
In the United States, a popular vote on a measure is referred to as a referendum only when originating with the legislature. An initiative may be called a “ballot measure”, “initiative measure”, or “proposition”.
The United States has no initiative process at the national level, but the initiative is in use at the level of state government in 24 states and the District of Columbia, and is also in common use at the local government level.
In the United States, [People’s Veto] exists, as of May 2009, in 23 states and one territory: Alaska, Arizona, Arkansas, California, Colorado, Idaho, Maine, Maryland, Massachusetts, Michigan, Missouri, Montana, Nebraska, Nevada, New Mexico, North Dakota, Ohio, Oklahoma, Oregon, South Dakota, Utah, Washington, Wyoming and the U.S. Virgin Islands. The popular referendum [or People’s Veto] was first introduced in the United States by South Dakota in 1898, and first used in the United States in 1906, in Oregon, two years after the initiative was used (in 1904, also in Oregon).