Fresh off a budget deal triumph, Sen. Patty Murray may be tempted to use her seniority to leave the Budget Committee chairmanship next year to succeed retiring Sen. Tom Harkin as chairwoman of the Health, Education, Labor and Pensions Committee.

If the Washington Democrat decides to do that, she also would likely succeed the Iowa Democrat as chairwoman of the Appropriations Labor-HHS-Education Subcommittee.

Should Murray make the move, the chairmanships of both chambers’ Budget committees could turn over at the same time, just as lawmakers begin work on the fiscal 2016 budget.

House Budget Chairman Paul D. Ryan, R-Wis., has expressed interest in seeking the chairmanship of the Ways and Means Committee next year. But Michigan Republican Dave Camp, the current chairman, has not said whether he plans to seek a waiver to serve another term as chairman. Under House GOP term limits, committee heads are limited to three terms as chairman, ranking member or a combination of the two. Camp plans to seek re-election this year in his district.

Sources in the budget community have been hearing Murray plans to switch. The fourth-term senator, who also serves as Senate Democratic Conference secretary and gained new prominence on Capitol Hill for her leadership last year on her party’s budget priorities, has given no indication of her plans.

“Chairman Murray is focused on her work in the Budget Committee and is not going to speculate about or comment on her role in future Congresses,” spokesman Eli Zupnick said recently.

But it makes sense to some analysts that Murray, with her strong interest in domestic policy, would want to make her mark on the HELP Committee.

Part of the reason is that the prominence of the Budget Committee may recede over the next couple of years.

In the budget deal in December, Congress set a discretionary spending limit for fiscal 2015 that will serve in lieu of a budget resolution if none is adopted. The 2011 Budget Control Act also established spending caps for subsequent years through 2021.

Despite the budget agreement reached by Murray and Ryan, many expect continued budget stalemate in coming years.

The 2014 midterm elections are another factor.

Republicans believe they have a shot at capturing control of the Senate, though Democrats could just as easily retain the majority. If the GOP prevails, the Democratic ranking member of the HELP Committee would wield more influence over policy in the more active HELP Committee than a ranking member of the Budget Committee.

Murray is outranked in seniority on the HELP Committee by Maryland Democrat Barbara A. Mikulski, who is second to Harkin. But Mikulski is unlikely to leave her powerful post as Senate Appropriations chairwoman, especially after her successful negotiation of a fiscal 2014 omnibus spending bill with House Appropriations Chairman Harold Rogers, R-Ky.

Were Murray to eschew the top Democratic position on HELP, Vermont independent Bernard Sanders, one of the most liberal lawmakers in the Senate, would be next in line.

Murray ranks second in seniority to Harkin on the Labor-HHS-Education Subcommittee.

The most likely successor to Murray if she steps down from the Budget Committee chairmanship is Florida Democrat Bill Nelson, who is third in seniority after Murray. Ron Wyden, D-Ore., is second in seniority to Murray on Budget. But Wyden is expected to assume the chairmanship of the powerful Finance Committee next year upon the retirement of Max Baucus, D-Mont.

Nelson, elected to a third term last year, currently serves as chairman of the Senate Aging Committee.

Smith characterized Nelson as “competent, careful and a team player,” adding that his home state of Florida is an important one for Democrats.