The Republican-controlled House has already voted 37 times to repeal or significantly change all or part of the Affordable Care Act of 2010, which the GOP likes to call Obamacare. Time No. 38 and possibly 39 are expected Wednesday evening as the House votes on legislation that would delay two key parts of the new health-care law for another year. President Obama has already said that he will veto both of these bills.

A Tea Party member reaches for a pamphlet titled "The Impact of Obamacare", at a "Food for Free Minds Tea Party Rally" in Littleton, New Hampshire in this October 27, 2012 file photo. (REUTERS/Jessica Rinaldi)

The new law requires most Americans to have health insurance starting on Jan. 1. It also requires businesses with at least 50 full-time employees to offer affordable, accessible health insurance or face heavy fines, a mandate originally set to begin next year.

But earlier this month, the White House announced that businesses will get an additional year before penalties start. The administration has said that this provides needed time for the government to simplify the reporting process that businesses and insurance companies will eventually use.

House Democratic Leader Nancy Pelosi has downplayed the impact of this delay, saying at a press conference last week that it will not slow implementation of the new law. White House spokesman Jeff Carney has said that roughly 96 percent of employers already offer some form of health insurance.

But Republicans seized upon this delay, seeing it as yet another weakness in Obamacare. Representatives introduced two bills that will be voted upon on Wednesday evening: One calls for a one-year delay for employers, the action that the Obama administration has already taken despite Republicans stating that the executive branch does not have the power "to write or rewrite law at whim." The second bill calls for a one-year delay on the requirement that nearly all Americans buy health insurance.

The White House said in a statement that the first bill is "unnecessary" and the second would increase health insurance premiums and the number of uninsured people.

House Speaker John Boehner (R-Ohio) said at a press conference last week that the administration's planned delay is "unfair and indefensible."

"Is it fair for the president to give American businesses an exemption from the law's mandates without giving the same break to individuals and families across the country?" Boehner said. "Hell no it isn't."