Democrats are seeking equality of outcomes instead of equality of opportunity, said Senator John Barrasso, a Wyoming Republican.
"Tax increases won't help our fragile economy, and they won't put the brakes on Washington's out-of-control spending," he said.
The Republican-controlled House of Representatives is also using today's tax-filing deadline to highlight tax policy. The House is scheduled to vote later this week on a $46 billion, one-year tax cut for businesses with fewer than 500 employees.
Under the bill sponsored by Majority Leader Eric Cantor, a Virginia Republican, companies would be able to deduct as much as 20 percent of their profits.
The Buffett rule bill is S. 2230. The House tax bill is H.R. 9.