The House Freedom Caucus wants to see Republicans have the ability to pursue changes in next year's budget that go beyond reforming the tax code.
Rep. Mark Meadows of North Carolina told Roll Call the conservative group is pushing for the GOP to have more authority.
"We believe that writing the instructions more broadly will give us greater flexibility not only to get tax reform but also to address other areas simultaneously," the Freedom Caucus chairman told the website.
The move would be part of the budget reconciliation process, which gives the authority for lawmakers in the Senate to pass bills that come from the House via a simple majority.
According to Roll Call, examples of where the legislative authority could come into play include welfare reform and changes to entitlements.
The House Freedom Caucus has made headlines in recent months, most notably because of its opposition to the original version of the American Health Care Act. After the bill was revised, Freedom Caucus members voted for it and helped get it passed over to the Senate.
A report last week, meanwhile, claimed the Freedom Caucus is taking an active role in tax reform and is writing a draft of a bill to present to House leadership.