Jefferson City, Mo. ? More than 1 million people are expected to participate in what amounts to the largest-ever public opinion poll on the nation’s new health care law.

Missouri on Tuesday will become the first state to the test the popularity of President Barack Obama’s top policy accomplishment with a statewide ballot proposal attempting to reject its core mandate that most Americans have health insurance.

The legal effect of Missouri’s measure is questionable, because federal laws generally supersede those in states. But its expected passage could send an ominous political message to Democrats seeking to hang on to their congressional majority in this year’s midterm elections.

The Missouri measure, shepherded to the ballot by Republican state lawmakers, is a glaring example of the twisting, troubled politics surrounding the health overhaul. After years of campaigning for health care reform, Democrats finally accomplished it. Yet Democrats are largely silent and it is Republicans who now are highlighting the health care law in their campaigns.

From Florida to Washington and numerous states in between, Republican candidates for the U.S. Senate and House — and even for local offices that have little to do with the federal law — are calling for the repeal of what they derisively dub as “Obamacare.”

A year after raucous town-hall forums, and months after Obama signed it into law, the health care overhaul remains divisive and national polls differ on its popularity. A Kaiser Family Foundation poll found approval grew to 50 percent while disapproval shrunk to 35 percent in July. A Pew Research Center poll showed the opposite, with approval falling to 35 percent and disapproval rising to 47 percent.

In the swing state of Missouri, where Obama narrowly lost to Republican Sen. John McCain in the 2008 presidential elections, the federal health care law appears particularly unpopular.

Sixty-one percent of respondents to a Mason-Dixon poll conducted this month for the St. Louis Post-Dispatch and TV station KMOV said they opposed the federal health care law. Opinion generally split along party lines, but among the key category of independents, 65 percent said they disapproved.

If passed by voters, the proposed Missouri law would prohibit governments from requiring people to have health insurance or from penalizing them for paying health bills entirely with their own money. That would clash with a key provision of the new federal law requiring most Americans to have health insurance or face fines starting in 2014.