By Elise Viebeck - 03/06/13 01:38 PM EST
The PCIP is designed to offer insurance to vulnerable patients while the rest of the law's provisions, including a ban on discrimination against pre-existing conditions, kick in next year.
To qualify, patients had to be without coverage for at least six months.
Tuesday's letter is notable given Republicans' staunch opposition to healthcare reform and their more than 30 attempts to repeal, defund or dismantle it.
Since the election, GOP lawmakers have stepped back from those efforts. The proposed continuing resolution to fund the government maintains money for the healthcare law, for example.
The letter stated that the House GOP remains fully committed to repealing the Affordable Care Act, saying the law is "driving up healthcare costs and making it harder for small businesses to create jobs."
"But," the members wrote, "our disagreement on the broader issues of the law should not preclude us from working together to take this specific action."