WASHINGTON — Republicans are pushing toward Senate approval of legislation demolishing President Barack Obama’s signature health care law and halting Planned Parenthood’s federal money, setting up a veto fight the GOP knows it will lose but thinks will delight conservative voters.

The White House promised a veto Wednesday, saying the bill would “take away critical benefits and health care coverage” from families. With Republicans lacking the two-thirds House and Senate majorities needed for a successful override, the measure became a political messaging battlefield as both parties looked toward the 2016 presidential and congressional elections.

“Obamacare is a direct attack on the middle class of our country. It’s a partisan law that puts ideology before people, that hurts many of the very Americans it was supposed to help,” said Senate Majority Leader Mitch McConnell, R-Ky., using the nickname for a statute that Republicans have uniformly opposed since Obama began pushing it through Congress six years ago.

Lawmakers have voted dozens of times to repeal all or parts of the health care overhaul. If the House, as expected, sends this bill to Obama, it would be the first to reach the White House and get vetoed. Republicans say such a scenario would highlight GOP priorities for voters.

Republicans fault the law for rising health care premiums and deductibles and a diminished choice of insurance providers in some markets. On Wednesday, government officials said health care spending grew last year at 5.3 percent, in part because of the health law’s coverage expansion, the steepest climb since Obama took office.

With GOP leaders insisting they had the votes they’d need, Sen. Mike Lee, R-Utah, said he’d support the bill, saying it “lays the groundwork for Obamacare to be erased from the books altogether.”