In the end, the Republican chairman said he was persuaded by arguments from House Budget Committee Chairman Paul RyanPaul RyanSanders set for clash with Trump’s budget pick Is healthcare law really going into a ‘death spiral’? Trump hosts Hill leaders for ice breaker MORE (R-Wis.) that defunding the law would save money, and rejected the Democrats' point of order.

The technical battle reveals once again the huge gap in the faith that both parties have in CBO estimates. Democrats have argued before that Republicans are essentially ignoring the CBO, which they say is the only neutral arbiter that Congress can rely on for budget estimates.

Republicans, on the other hand, have argued that CBO estimates are not accurate because they rely on faulty assumptions that Congress provides. Sen. John McCainJohn McCainSenate panel votes to confirm Tillerson Overnight Defense: Trump nominates Air Force secretary | Senate clears CIA director | Details on first drone strike under Trump McCain: Trump's withdrawal from TPP a 'serious mistake' MORE (R-Ariz.) in January summed it up this way: "Garbage in, garbage out."

Democrats today charged Republicans with selectively interpreting their own rules in order to favor Republican amendments. Rep. Robert Andrews (D-N.J.) said the acting chairman should not rely on Ryan's assessment, and Rep. Frank Pallone Jr. (D-N.J.) said the way the ruling is made is "sort of like a one-man dictatorship."

After the procedural battle, the House turned to an hour of debate on the Rehberg amendment.

"My goal, and the goal of the majority of Americans, is to repeal the healthcare law," Rehberg said. "Until then, my objective is to defund it entirely and stop its implementation."