Key Republican opposes health bill because of pre-existing conditions coverage

According to an ABC News whip poll, 21 Republicans currently oppose the bill.

"I’ve supported the practice of not allowing pre-existing illnesses to be discriminated against from the very get go," Upton said. "This amendment torpedoes that."

"What's important is we want to have a situation where people can afford their health insurance. We want to have a situation where people have a choice of health insurers. That's not happening in Obamacare," Ryan said, pointing to high premium increases. "So what good is insurance if you don't get it, if it's not offered to you or you can't afford it? So the purpose of our bill is to get more choices to lower prices while preserving the protections for pre-existing conditions. So that is a very important thing."

"We're excited about this policy," he continued. "We're making very good progress with our members and our president has been instrumental to that."

According to ABC News' whip count, at least 21 Republicans are opposed to the amended health care bill, putting the GOP on the verge of losing a potential vote.

Even more Republicans remain undecided on the measure, including Rep. Ed Royce, R-California, the chairman of the House Foreign Affairs Committee, and Rep. Rodney Frelinghuysen, R-New Jersey, the chairman of the House Appropriations Committee.

A House GOP aide said a vote this week, before the House leaves Washington for a week-long recess, is a possibility, though no changes had been made to the schedule as of Tuesday afternoon.

The aide said Republican leaders are considering adding more funding to the high-risk pools for consumers with pre-existing conditions, in an effort to court more GOP moderates.

This morning, top Republicans were mum on a potential vote this week. Leaders didn't bring it up in the GOP conference meeting, according to members. House Majority Whip Scalise told reporters the whip count is "better" today.

"We’re still trying to work through some issues," Rep. Dave Reichert, R-Washington, told reporters as he left Pence's meeting.