WASHINGTON, Jan 2 (Reuters) - Conservative activists opposed to President Barack Obama's healthcare overhaul started a new assault on the Affordable Care Act as more than 2 million people began new health coverage under the law on Thursday.

One group, which is backed by the libertarian billionaire brothers Charles and David Koch, launched a $2.5 million television ad campaign that targets three Democratic senators who support the law and could face stiff challenges from Republicans in November elections.

The group, Americans for Prosperity, or AFP, spent more than $36 million on the 2012 elections, largely for ads that bashed the law known as Obamacare and Democrats who supported it.

The ads by AFP are aimed at North Carolina's Kay Hagan, Louisiana's Mary Landrieu and New Hampshire's Jeanne Shaheen. Their bids for re-election will be crucial to Democrats' efforts to keep control of the U.S. Senate, where Democrats control 55 of the 100 seats.

The 30-second videos represent something of a turn in strategy for conservatives, who have spent much of the past year focused on calling for the repeal of the healthcare law, the most sweeping social program since the 1960s.

Now, with more than 2 million people having signed up for Obamacare and more enrolling for coverage every day, AFP and other critics are signaling that in advance of the elections, they will try to cast Democrats as liars who misled Americans about the law.

The new ads try to link the senators to Obama and his discredited pledge that all Americans who liked their healthcare plans before Obamacare went into effect could keep those plans.

In fact, the minimum coverage standards imposed by the healthcare law meant that hundreds of thousands of people with inexpensive, bare-bones policies had their policies canceled. They will have to buy coverage that in some cases is more expensive. Federal subsidies will help many low-income Americans make that transition.

For years, Obama had said that "if you like your current insurance, you keep your current insurance." But in early November he acknowledged that some would not be able to keep their policies and apologized for understating the law's impact on those people.

His initial statements were dubbed the "Lie of the Year" by the PolitiFact fact-checking website.

The ads are the latest anti-Obamacare push by the AFP, which since August has spent nearly $19 million on TV messages targeting Democrats who support the law. It was passed in 2010 to help millions of uninsured and under-insured Americans, but Republicans have opposed the reform as an unwarranted expansion of the federal government and say it is too costly and eliminates healthcare choices for many.

In the AFP ad aimed at Hagan, a North Carolina woman whose insurance plan was canceled talks directly to the camera.

"Kay Hagan told us, 'If you like your insurance plan and your doctor, you can keep them.' That just wasn't true," she says. The Shaheen and Landrieu ads feature the senators repeating Obama's claim.

In a statement, Landrieu's campaign called the AFP ads a "grossly misleading" distortion of her efforts to improve the healthcare law.

Hagan's office said it was "a new year and a new smear from a Koch brothers-backed group that has no accountability to North Carolinians."

AFP president Tim Phillips said the ads would run for up to three weeks. "We believe that repealing Obamacare is going to be a long-term effort, and this is part of that long-term effort," he said. (Editing by David Lindsey and Grant McCool)