In the end, the Republican chairman said he was persuaded by arguments from House Budget Committee Chairman Paul RyanPaul RyanGOP grapples with how to handle town halls Leaked ObamaCare bill would defund Planned Parenthood House markup of ObamaCare repeal bill up in the air 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 McCainDrug importation won't save dollars or lives Dem rep Charlie Crist files for divorce Why the GOP cannot sweep its Milo scandal under the rug 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."