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.