Updated

A Democratic senator said Tuesday that a deal made between New Hampshire Sen. Judd Gregg and his state's Democratic governor to name a Republican to replace Gregg in the U.S. Senate was "alarmingly undemocratic."

Gregg, the Republican picked by President Obama to be commerce secretary, is "well qualified" for the post, Sen. Russ Feingold, D-Wis., said, but he thinks  but "the apparent behind-the-scenes deal-making that went on to determine who will fill Sen. Gregg's vacancy is alarmingly undemocratic.

"Once again, Americans will be represented in the Senate for nearly two years by someone they had no hand in electing," Feingold said.

Feingold last month proposed a constitutional amendment to require Senate vacancies be filled by popular election rather than by gubernatorial appointment after then-Illinois Gov. Rod Blagojevich named Roland Burris to replace Obama in the U.S. Senate. Feingold repeated the call Tuesday.

"As the number of senators appointed to their seats continues to rise, its increasingly clear that we need to fix this constitutional anachronism. It is time to pass a constitutional amendment to end appointments by governors and the political gamesmanship they encourage," he said.

Obama announced Tuesday that Gregg would become his nominee as commerce secretary. Barring a major revelation, Gregg should have no problem getting confirmed.

But his departure sets up a vacancy in the Senate, which caucuses with a 58-41 Democratic advantage.

If New Hampshire Gov. John Lynch, a Democrat, were to replace Gregg with a Democrat, and if Al Franken defeats Norm Coleman in the disputed Minnesota race, then the Democrats would gain a filibuster-proof 60-seat majority.

Gregg said he refused to accept the post if that happened, and won assurances from Lynch that a Republican would be named to succeed him. Former Gregg aide Bonnie Newman is expected to be appointed to Gregg's seat.

FOX News Radio's Mike Majchrowitz contributed to this report.