"The President feels very strongly about including this at some step," Brady said at the Politico event.
In recent days, President Donald Trump has made clear that he wants lawmakers to look at the possibility of adding in provisions on the Obama health law as well - nothing on Obamacare was included in the original draft of the tax reform bill.
When it comes to the GOP effort to overhaul the Obama health law, which ran aground earlier this year, there would be no parliamentary impediment to adding some of those health care provisions to this bill, as long as they followed the rules under budget reconciliation, and that the overall tax reform bill does not increase the deficit by more than $1.5 trillion over the next ten years.
The Congressional Budget Office has found that repealing the individual mandate penalty under the Obama health law would decrease the deficit by $416 billion over ten years, meaning the inclusion of that provision could help 'pay for' other tax cuts.
That same report from the CBO says that getting rid of the individual mandate would also have a broader impact, causing "a substantial reduction in the number of people with health insurance."