When the human beings populating Congress had integrity they sent up bills as line items. They figured out that was too empowering of the President and "fixed" things with all-or-nothing kitchen sink piles-of-paper.
Anything fixed in Congress via this method she proposes can be undone just as quickly. Reagan fought for a line item veto for his entire time in the White House and they told him to pound sand.
Not saying she shouldn't try, maybe the conversation would be helpful, but she has no juice down there. If she had Ryan and McCarthy on her side it would help. If they refuse she could make a big stink about it ( but I'll bet she won't ). She could get external expertise from Gingrich and other alumni and start a movement.
Alas, these things are only going to get solved through We The People setting new iron-clad rules for Congress and the entire FedGov through a series of Amendments. It is the only way to be sure. However, I fear it is too late.
That's why many of us are working on the Convention of States Article V project. I hope you are too.