Thompson, the ranking Democrat on the House Homeland Security Committee, told The Associated Press on Tuesday that he is seeking re-election next year.
"The good thing about America is that people have choices," Thompson said in a written statement. "Those who are qualified and wish to seek public office can. I am busy protecting the district's interests in the upcoming Farm Bill, and fighting to save Head Start, Medicare, Medicaid and Social Security from Republicans who are trying to end those programs.
"I look forward to continuing my work with local elected officials who have demonstrated a commitment to bettering their communities," he said.
Hudson was attending a fundraiser Monday night in New York and said she has hired a national Democratic political strategist and pollster, Celinda Lake.
Thompson faced his last significant Democratic primary challenge in 2006, when he received about 65 percent of the vote to defeat state Rep. Chuck Espy of Clarksdale.
Thompson won the 2006 general election with roughly the same margin over Republican Yvonne Brown, who had been mayor of Tchula.
Mississippi has four U.S. House districts and the 2nd is the only one with a majority-black population. Historical voting patterns show Republicans struggle in the district. In November, Thompson easily defeated Bill Marcy of Vicksburg, a black Republican who courted tea party voters.
Thompson and Hudson are black, as are Espy and Brown.
Thompson ended 2010 with nearly $1.7 million in his campaign fund, according to his latest report filed on the Federal Election Commission website.
Kathie Stromile Golden, a political scientist and head of the international studies program at Mississippi Valley State University, said Tuesday that no member of Congress, including Thompson, should be surprised by drawing an opponent.
"I think quite a few people will be excited by the fact that here you have a black female who currently holds a political position who has some national exposure," Stromile Golden said of Hudson. "She's known within the Democratic Party. She's young and she's energetic."
Hudson, who's now in her mid 30s, was elected Greenville mayor in 2003 and 2007. She said in January that she won't seek a third term.
Thompson, 63, was chairman of the House Homeland Security Committee from 2006 through 2010, when Democrats held the majority. With Republicans now in the majority, he's the committee's ranking Democrat.The 2nd District is more than 200 miles long, stretching through the cotton and soybean fields and catfish pond areas of the historically poor Delta. The district wanders through the Civil War battlefields of Vicksburg and down past the Grand Gulf nuclear power plant in the woods outside Port Gibson. The district also encompasses most of Jackson.
If anyone in Mississippi could beat Bennie Thompson, it might well be Heather... particularly after a few phone calls from "Daddy". She has all of the qualifications: black, female, rich daddy with political pull, and a proven track record of incompetence in city government! What more could we wish for?
Bennie takes a more "optimistic" view of this situation stating that in America, we still have choices... and he is quite right. As the political satirist Lewis Black so aptly states, "we now have a choice between two bowls of shit."
Either way, for Greenville, this will be a win-win decision. We will have proven that "black, female, and well educated" are not the essential qualities of a good mayor for our city... and we will save thousands of tax-payer dollars on eliminating body guards!
"Heather goes to Washington"... what great potential for a movie sequel! I can see it now as the black screen illuminates into early dawn... the sun rising in the distance as the camera pans slowly onto a parked pick-up truck in Arlington... Cemetery...