In May, he said he would want to "deal with these issues on a ... permanent basis as opposed to a stopgap effort that would require unraveling and re-evaluation," he said.
Romney opposes the nearly $500 billion in cuts to defense spending called for under the so-called sequester. And he doesn't want the Bush-era tax cuts to expire for anyone.
At the same time, he has promised to balance the budget in eight to 10 years without cutting defense or raising taxes.
Lawmakers and policy experts say the best a lame-duck Congress can probably do before the end of the year is come up with a "bridge" or "framework" deal.
Broadly, that might mean lawmakers postpone fiscal cliff measures for several months to a year, negotiate a small amount of spending cuts and agree to strike a large deficit-reduction deal by a date certain next year, perhaps according to agreed-upon targets for spending and revenue.
But then if lawmakers failed to deliver next year, the fiscal cliff or something similar would take effect.
- Jessica Yellin, CNN's senior White House correspondent, contributed to this report.