President Obama could have been more vigorous in pressing for middle-class tax cuts, the second-ranking House Democrat said Thursday in a show of frustration.

Outgoing House Majority Leader Steny Hoyer (D-Md.), who will serve as minority whip in the next Congress, publicly voiced his disappointment in the White House for not having fought Republicans more before striking a deal on tax cuts.

"I'm disappointed that we didn't make a more vigorous fight," Hoyer said on MSNBC.

Democrats have openly voiced their frustration toward the White House this week since the administration struck a deal with Republicans to extend all tax cuts for two years, in exchange for extending some tax breaks and unemployment insurance.

"Do I think the president could have perhaps done that more vigorously? Yes," Hoyer said. "Does my caucus think that was the case? Yes."

The administration has launched an all-out effort to drum up support for its tax-cut compromise, and Vice President Biden headed to Capitol Hill on Wednesday evening to try to sell House Democrats on the plan. But liberals and some centrists in the party continue to publicly vent their frustration toward the administration, specifically for its compromise on the estate tax.

Hoyer said he would have preferred for the administration to press for a "full-fledged filibuster" in the Senate when it voted down two Democratic-backed proposals that would have extended middle-class tax cuts, but let rates go up for top earners.

An effort like that, the No. 2 House Democrat argued, would have maybe satisfied more members of Obama's party on Capitol Hill that the administration was willing to fight for its initial stance on tax cuts.

"I think we're all frustrated that we could not adopt policies that are consistent with what the overwhelming majority of Americans think is good, sound policy," Hoyer said.