After years of trying to repeal Obamacare, Republicans are planning a new strategy to eliminate some of the law's most unpopular provisions by using targeted legislation with the potential to attract enough Democratic votes to reach President Barack Obama's desk.

First they have to pick up the six seats they need for a U.S. Senate majority in Tuesday's midterm elections, which would give the party control of both congressional chambers for the first time since 2006.

With opinion polls showing the odds for Senate control increasingly in their favor, Republicans are exploring a series of efforts to repeal some of Obamacare's taxes and penalties on businesses.

The Affordable Care Act, Obama's signature domestic policy achievement, aims to reduce the number of uninsured Americans by offering subsidized private coverage to lower income Americans and by extending Medicaid program for the poor.

But the law has been a target for constant Republican attack since Congress enacted it in 2010, when both chambers were controlled by Democrats. Republicans view it as an unworkable expansion of big government that will only raise healthcare costs while hurting businesses, job growth and the economy.

A Republican-controlled Congress would still be expected to kick off in January with separate bills to repeal the entire law, as well as the penalty for individual Americans who fail to obtain health coverage and the federal subsidies for low-income people enrolled in private Obamacare health policies.

Senate Republican Leader Mitch McConnell came under fire from conservatives critics last week after saying the party was unlikely to have the 60 Senate votes, out of 100, needed to repeal the law with standard legislation. A McConnell spokesman said his position had not changed: a Republican-controlled Senate would still see a full repeal vote and McConnell remained committed to undoing the law's funding provisions through a special parliamentary process requiring only a simple 51-vote majority.

But with a White House veto of such measures all but certain, Republicans hope to move on quickly to legislation capable of drawing enough Democrats to surmount the Senate's legislative hurdles and put pressure on Obama to acquiesce, lawmakers and aides said.

Chief among Republican targets is the ACA's employer mandate, which requires businesses with at least 50 full-time workers to offer health coverage to their employees or pay a penalty. Also on the hit list are the law's definition of "full time" as any employee who works 30 hours a week or more, provisions that compensate health insurers for market losses and an excise tax on medical devices, including the machines that produce CAT scans and magnetic resonance images.

"There's consensus that we need to tear down the most destructive parts of the law that are hurting people and are hurting our economy. And there's proven bipartisan support for some of our ideas," said Senator John Barrasso of Wyoming, an orthopedic surgeon and a leading Republican voice on healthcare.

Employer requirements and taxes have also been the subject of intense lobbying by the business community, including medical device manufacturers, while risk provisions that seek to reduce insurer losses have become a favorite target for Tea Party-backed conservatives who warn of a looming government "bailout" for the insurance industry.

Some measures have won support from senators in both parties, including Republican Orrin Hatch's budget resolution amendment last year to repeal the excise tax on medical devices. That measure was blocked from a later floor vote by Democratic leaders.

There also could be room for negotiations between parties once the repeal efforts run their course. Democratic Senate aides say they have talked to Republican aides about compromises including streamlining reporting requirements for employers and replacing the tax penalty with an incentive for firms to offer health coverage to workers.

Both parties could add proposals to tweak Obamacare to broader pieces of legislation, such as a budget or appropriations bill.

"That is the old fashioned way of passing legislation. You pull together a bunch of things that could have gone separately, you find a way to pay for them and you get enough people to hold their noses and vote for it," said Joe Antos of the conservative American Enterprise Institute.