"I would like to link any change in the reimbursement mechanism to real structural reforms," said Boustany, the chairman of the Ways and Means subcommittee on oversight.
Hospitals are picking up about half the tab for the most recent doc fix, which cost about $30 billion.
The deal was negotiated as part of the bill avoiding the "fiscal cliff" at the beginning of the year.
Without a fix, Medicare physicians would have seen a substantial pay cut under the SGR.
Repealing the formula is now "on sale," Brady said Tuesday, citing a recent budget report that said SGR repeal would cost $107 billion less than previously estimated.
Brady and Boustany addressed the Federation of American Hospitals at its annual policy conference in Washington.
"We will need your help in supporting the structural changes," Brady told the gathering. "If you want to stop this continued reliance on provider cuts, we're going to need your support in major way."
At another recent conference, House Energy and Commerce Committee Chairman Fred Upton (R-Mich.) said he will fast-track an SGR repeal bill with the goal of floor action in July or early August. Read more about those remarks at Healthwatch.