At the start of a hearing this week, U.S. House Budget Committee Chairman Tom Price noted the “diligent work” of the head of the Congressional Budget Office, seated before him.

Left unsaid was Price’s likely move to sack Douglas Elmendorf amid a debate about the benefits of tax cuts and lingering scars from the tortured process to pass Obamacare.

Partisan tugs of war over the leadership of the CBO are nothing new, but critics are saying that the Republican emphasis on “dynamic scoring” — which would take into account broad economic impacts of pending bills outside the scope now examined — is imprecise and could threaten the CBO’s reputation as an impartial scorekeeper.

The stakes are high: The CBO’s “scores” on legislation’s fiscal impact can buoy or kill a bill.

But Price and other conservatives say CBO scores are inherently inaccurate when they do not take into account how new tax laws shift the economy — instead just adding up the dollars lost or gained for the government under present, vacuum-sealed conditions.

“The Congressional Budget Office is, I believe, imprisoned by rules right now that make it so they can’t get to the right answer,” Price said in a speech this month at the conservative Heritage Foundation think tank.

Bloomberg News reported in December that Republicans will not reappoint Elmendorf now that they control both chambers of Congress. Price has told the Hill newspaper he is "working through a process" on the CBO. A Price spokesman would not provide a timetable for a final decision.

Price, along with Senate Budget Committee Chairman Mike Enzi, R-Wyo., and House and Senate leadership, will make the call.

Elmendorf, who has been in his post since 2009, politely declined to comment Tuesday to The Atlanta Journal-Constitution on his job situation.

At Tuesday’s hearing, U.S. Rep. Chris Van Hollen of Maryland — the Budget Committee’s top Democrat — sought to undermine dynamic scoring in his questions to Elmendorf “so we understand what the implications are and what the limitations are with respect to current models.”

Elmendorf testified that dynamic scoring does not take into account the effect of income inequality, which some research has shown can hamper economic growth.

At the start of the Congress, Republicans passed new rules to allow for dynamic scoring from the CBO and the Joint Tax Committee in certain cases. But the conservative distaste for the CBO extends to the Obamacare debate.

The CBO played an outsized role in the law's crafting, including selling it as not a budget-buster. In the end, the CBO's projection showed that the Affordable Care Act would reduce the deficit over a 10-year window — because the law included tax increases and cuts to the growth of Medicare for all 10 years, while not paying out subsidies on the health insurance exchanges until four years in. Last year Elemendorf repeated his projection that Obamacare would reduce the deficit.

MIT professor Jonathan Gruber, the former White House adviser whose statements about the health care law caused a stir last year, said that the CBO's determination that the health insurance mandate was not a tax was critical to the law's passage. Critics accused Elmendorf of being too willing to take Gruber's — and thus the White House's — view of how the law would play out in terms of coverage and premiums.

“If you think about what’s happened under Elmendorf’s tenure, what we’ve known about Obamacare scoring, the misleading nature of that, all that stuff is grounds for saying we need somebody new,” said Dan Holler of Heritage Action for America, the advocacy arm of the think tank.

Democrats have pushed to keep Elmendorf. Prominent Senate Democrats, including U.S. Sens. Charles Schumer, D-N.Y., and Elizabeth Warren, D-Mass., wrote a letter to Price and other GOP leaders claiming that replacing Elmendorf “would fundamentally compromise the integrity of an institution that has served as a trusted scorekeeper.”

They cited former George W. Bush administration economist Greg Mankiw, who urged the GOP to keep Elmendorf, saying the director has "shown himself to be scrupulously nonpartisan."

Holler countered that this idea of the CBO is antiquated.

“Most people — Republicans and Democrats, conservatives and liberals — use the CBO numbers when they work to validate a point and they ignore CBO when whatever information they come out with is contrary to their standpoint,” Holler said.

Stan Collender, a former Capitol Hill staffer and federal budget expert at Qorvis Communications in Washington, said partisan fights over the director go back to the 1970s when the CBO was created. He said the key test for Elmendorf’s likely successor is whether that person keeps the office’s effective longtime senior staff in place or loads it up with “partisan hacks.”

But for Republicans, the fight is also about sending a message to their base.

“This is symbolic more than anything else,” Collender said. “This is appeasing conservatives who think they have been screwed by the budget rules for years.”