Senate Minority Leader Chuck Schumer, D-N.Y., argued Wednesday that a new amendment to the American Health Care Act that has earned the support of the House Freedom Caucus would violate a Senate rule requiring budget reconciliation bills to deal strictly with budget matters.

If true, that would likely make it harder for Republicans to partially repeal and replace Obamacare using the budget reconciliation process.

A spokesman for Schumer claimed that the amendment, which was brokered by Reps. Tom MacArthur, R-N.J., and Mark Meadows, R-N.C., would violate the "Byrd Rule," and therefore require 60 votes for passage instead of the 51 votes Republicans are hoping for instead under the reconciliation process. Budget reconciliation bills need fewer votes, which is why the GOP is trying to pass its Obamacare bill under the framework of reconciliation.

"Once again, House Republicans have made their bill worse for the health of the American people in order to buy off the Freedom Caucus and other conservatives. But once again, that effort is almost certainly going to run afoul of Senate reconciliation rules, ensuring that the bill with these provisions will need 60 votes to pass," said Matt House, a spokesman for the Senate Democratic leader. "There will not be 60 votes for a bill that drives up premiums and causes millions of people to lose their health insurance."

House argued that the policy and budgetary effect of the amendment is incidental, which means it would have stripped out. The amendment to the AHCA allows states to opt out of requiring insurers to cover essential health benefits, but requires insurers to cover individuals with pre-existing conditions.

Senators may invoke the Byrd Rule, a 1990 amendment to the Congressional Budget Act of 1974 that calls for the removal of language in budget reconciliation bills that are "extraneous" to the budget, in an effort to reduce the inclusion of policy issues that might only incidentally have a budget impact.

Republicans are hoping the language survives, and the decision will likely come down to the decision of the Senate parliamentarian. If the parliamentarian decides the language is extraneous, it would take 60 votes to overturn that decision, but a decision in favor of Republicans would be equally hard for Democrats to overturn.

"I'm not worried about that at all," said Rep. Joe Barton, R-Texas. "The Byrd Rule was put in place by Sen. Byrd to give the bird to the House ... If it doesn't have a primary financial impact it could be removed. If the primary benefit is to lower premiums, then that has a primary financial impact."

"The House should do what we think is the best public policy, send it to the Senate and then let the Senate deal with it," Barton said. "If we wet our pants every time somebody raises a question about the Byrd Rule then we'd never get anything done."

Robert King contributed to this report.