Updated: 11:58 a.m.

Sen. Judd Gregg (R-N.H.) acknowledged Friday morning that he is in the running for Commerce secretary, but he did not allay fears in his party that his exit from the Senate could give Democrats a filibuster-proof majority.

In a statement issued by his office, the ranking member of the Senate Budget Committee left open the question of whether he would take the position if President Barack Obama offers it to him.

“I am aware that my name is one of those being considered by the White House for Secretary of Commerce, and am honored to be considered, along with others, for the position. Beyond that there is nothing more I can say at this time,” Gregg said.

The prospect is tricky for Gregg, given that New Hampshire Gov. John Lynch is a Democrat who would have the power to name Gregg’s replacement. However, Democrats privately said Lynch’s strong independent streak made them nervous that he might not pick someone from his own party to fill the spot should it open up.

But if Lynch replaced Gregg with a Democrat, Senate Democrats would likely end up with a 60-vote majority, which would allow them to beat back GOP-led filibusters. That scenario depends on Democrat Al Franken being named the official winner in the contested Minnesota Senate race. Franken currently leads former Sen. Norm Coleman (R) by 225 votes, but the case is wending its way through state courts.

A solid conservative who is a close ally of Senate Minority Leader Mitch McConnell (R-Ky.), Gregg has been a strong supporter of the controversial government bailout of the financial industry. At Commerce, he would have a hand in creating Obama’s economic policy at a time when indicators show a deepening recession both in the United States and worldwide.

If tapped, Gregg would be the second GOP lawmaker to head to Obama’s Cabinet. The president selected then-Rep. Ray LaHood (R-Ill.) as his Transportation secretary.

Senate Republican Conference Chairman Lamar Alexander (Tenn.) said Friday that he hoped Gregg would decline the offer because of the political ramifications for Republicans as well as the prospect of losing one of the GOP’s top strategists and thinkers.

“I like the idea of 41 Republican Senators a lot better than 40, and I like the idea of Judd Gregg in the United States Senate, rather than him not being there,” Alexander said. “Although, I can understand why President Obama would want to recruit him. He’s a real statesman. He’s one of our very best Senators — widely respected on both sides of the aisle.”

Alexander said he talked to Gregg about the appointment and joked that he would mount a “friendly Republican filibuster” against the nomination should he be picked.

“I told him he was going to have a hard time getting confirmed if he left,” said Alexander.