Some groups are already offering potential tax policy changes that they hope Democrats will include on their list of must-pass legislation this year.

For example, nonprofit groups want Congress to take bipartisan action to improve the above-the-line tax deduction for charitable donations, said David Thompson, vice president of public policy for the National Council of Nonprofits.

"Most of our issues are bipartisan. Our challenge normally isn't partisan control, but partisan bickering," he said. "If they would stop fighting for fighting sake and pass what they agree on, we'd be fine."