Montana Rep. Denny Rehberg’s departure from Congress leaves vacant the chairmanship of an appropriations panel that figures prominently for Republicans who want to shrink the budget and gut the 2010 health care law.

The House Appropriations subcommittee overseeing the departments of Labor, Health and Human Services, and Education is in charge of the largest nondefense discretionary spending bill. And whoever serves as chairman after Rehberg would play a significant role in GOP attempts to cut off funding for President Barack Obama’s signature health care law, a strategy that is one of few weapons the GOP has left to interfere with its implementation.

At the same time, the chairman will face tough budgeting decisions in a spending-wary environment. And to stop the recent history of not passing a separate Labor-HHS-Education appropriations bill, the chairman will need to compromise with Democrats on the measure’s spending levels and many controversial provisions.

“It’s not the plum assignment it once was, and it’s a thankless job,” said Emily Holubowich, executive director of the Coalition for Health Funding, which represents public health organizations. “It’s fun to spend money; it’s not fun to cut everything.”

At least four names are in the mix to take over the chairmanship: Reps. C.W. Bill Young of Florida, Jack Kingston of Georgia, Mike Simpson of Idaho and Rodney Alexander of Louisiana. All but Young currently serve on the Labor-HHS-Education subcommittee.

John Porter, a former Labor-HHS-Education panel chairman now with Research!America, notes that, traditionally, Republicans go down the membership list of the full committee by seniority when selecting subcommittee chairmen.

Young is the most senior of the four on the full Appropriations Committee, and he is hitting term limits in his role as chairman of the Defense subcommittee. He could get a waiver to continue serving, or he could move to be the chairman of another subcommittee.

A former full committee chairman, Young also served on the health subcommittee for more than 20 years. He has been a vocal advocate for medical research and successfully campaigned to double the budget for the National Institutes of Health.

Kingston chairs the Agriculture subcommittee and Simpson is in charge of the Interior bill. Neither has reached his term limits on those panels and may not want to switch. Porter predicted they would want to stay in place.

“Mr. Kingston is willing to serve in any capacity that allows him to continue his pursuit of a smaller, more efficient federal government,” an aide to the congressman said in an email.

Alexander’s spokesman, Jamie Hanks, confirmed that the congressman is interested in the subcommittee chairman spot.

Alexander is particularly interested in medical research, an area in which Democratic and Republican appropriators have been able to find common ground. He has defended a program at the National Institutes of Health that gives medical research money to states with a poor track record of competing for grant money, including Louisiana.

He is also a fierce critic of the health care law (PL 111-148, PL 111-152) and was chosen to lead floor debate on a bill to block its implementation in 2011. If he becomes chairman, he could use the appropriations process to try to strike at the health care law as Rehberg did.

The subcommittee’s fiscal 2013 draft bill cut funding for several health care law provisions, including the Center for Medicare and Medicaid Innovation. And Republicans successfully cut money for the law’s Medicare cost-containment board in the fiscal 2012 omnibus appropriations package (PL 112-74).

But much of the law’s funding is mandatory, so appropriators can’t remove it. And while Republicans want to strike the law’s funding, Democrats in the House and Senate insist on protecting it, making it difficult to reach compromise.

“Many Republicans won’t vote for anything that has funding for the [Affordable Care Act]. So it’s just added a whole other layer of complexity,” Holubowich said.

One of the biggest challenges appropriators have these days, Porter said, is to push against calls to cut domestic spending across the board by the same amount.

“We’re in a period where the appropriators are going to be required to make cuts, and the last thing we ought to ever do is cut mindlessly, every single program the same,” Porter said. “The whole job of appropriators is to determine the priorities of the programs under the jurisdiction of their committee.”

If Young or Alexander becomes chairman and want to increase funding for medical research, for example, they will need to cut other programs to arrive at an acceptable total spending figure.

“It’s no fun to be slashing funding for CDC by 10 percent, or not being able to give NIH an increase,” said Holubowich, referring to the Centers for Disease Control and Prevention. “The overall fiscal environment makes it really hard to be an appropriator right now.”