WASHINGTON—Conservative House Republicans said Monday night that they have enough votes to block the GOP’s legislation to dismantle the Affordable Care Act, as House leaders proposed changes to the bill in a late effort to draw support.

Rep. Mark Meadows (R., N.C.), chairman of the House Freedom Caucus, a group of conservative lawmakers, said more than 21 members opposed the bill, enough to block passage should House leaders hold the vote as expected on Thursday and all Democrats hold firm in opposing the legislation.

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