(And by "Obama's budget", I mean the one unanimously rejected even by his own party.)
What are those "draconian cuts" that Paul Ryan has proposed in his budget? Is he really going to throw Granny off the cliff with his changes to Medicare?
The Independent Voter Network has an interactive graph where you can see the spending over the next 9 years with the two different budgets. You can also choose a specific area (Medicare, Social Security, interest on the debt, security, etc.) to see how that particular area is affected.
What you'll see is that, under the Ryan budget, spending increases every year. The "cuts" that Democrats and the media keep referring to use the typical DC definition. "If you don't raise spending on X as much as I want to, you are therefore "cutting" spending to X."
The one exception is Medicaid, where spending dips slightly early on, but over the 9 year span does indeed increase slightly.
Point your friends at this page when they start believing the Democratic talking points. We simply cannot have a rational discussion on the debt problem facing us if we demagogue what amounts to a tepid response to the problem.