WASHINGTON (AP) -- President-elect Barack Obama's Cabinet picks Monday are sweet political gifts for the Republican who'll become governor of Arizona and the yet-to-be-named Democrat who'll assume Hillary Rodham Clinton's Senate seat.

Under Arizona state law, the ascension of Democratic Gov. Janet Napolitano to Homeland Security Secretary will mean Arizona Secretary of State Jan Brewer will assume the reins there. In New York, Clinton's planned departure means Gov. David Paterson will have a month or more to choose a successor for her.

Rep. Nita Lowey, one of the more prominent potential Clinton replacements, told The Associated Press that she will remain in the House and not take Clinton's job.

The 71-year-old Lowey said she isn't interested in giving up her hard-earned seniority on the House Appropriations Committee - a position which happens to give her a great deal of say over the budget of the State Department which Clinton may soon lead.

"Even though it's a great honor to be considered, for me, it makes more sense and I can accomplish more for my district, the state, and the country, if I stay in the House of Representatives," Lowey said in a phone interview with The AP.

Clinton "would be an outstanding secretary of state and frankly in my position as the chair of the subcommittee that funds the Department of State and all foreign aid, I'm thrilled to have the opportunity to work with her in the future," Lowey said.

Lowey had been expected to seek the Senate seat back in 2000, but stepped aside for Clinton, then the first lady.

In New York, the next senator is almost certain to be a Democrat, and adopt many positions similar to Clinton. That is unlikely to be the case in Arizona.

Brewer, 64, is a veteran Republican officeholder, with more than two decades as a legislator, a Maricopa County supervisor and secretary of state. Arizona does not have a lieutenant governor.

Brewer had a reputation as a fiscal hard-liner and conservative on social issues while a legislator in the 1980s and 1990s, so her taking over the governorship would mean a new approach from Napolitano's direction. A spokesman for Brewer's office didn't immediately return a call for comment after Obama's official announcement.

The jockeying to replace Clinton in the Senate began well before the announcement; Gov. Paterson's decision not to make a decision on a successor until January likely means a frenetic holiday season for New York politicians.

"You can ask me this question a million times, I'm not getting into who the candidates are, what do I think of them," the governor said.

Among those mentioned as potential successors are New York Attorney General Andrew Cuomo, Buffalo Mayor Byron Brown, and a host of representatives in Congress.

Reps. Kirsten Gillibrand and Brian Higgins would satisfy those seeking someone from upstate New York. New York City contenders include Reps. Carolyn Maloney, Jerrold Nadler, and Nydia Velazquez. Rep. Steve Israel and county executive Tom Suozzi would presumably strengthen the Democratic state ticket in their vote-rich home turf of Long Island.

Then there are the longshots: environmentalist Robert F. Kennedy, Jr. and his cousin Caroline Kennedy. Former President Bill Clinton's spokesman, Matt McKenna, said Clinton won't succeed his wife in the Senate, calling the notion completely false and saying that Clinton is excited to expand the work of his foundation. Clinton's work has already led to agreements to provide lower-cost AIDS/HIV drugs to 1.4 million people worldwide.

Whoever is chosen will have to campaign in a special election in 2010, at the same time Paterson and New York's senior senator Charles Schumer are on the ballot. The seat would then come up for election again in 2012, when Clinton's current term would have expired.

"I do think it should be a woman," said Maloney, who called Obama's selection of Clinton "brilliant," and suggested Paterson look for a similar record of competence in "someone who will work their heart out in a very challenging time for the state."

Gillibrand said she thinks Paterson will seek "a good partner for Sen. Schumer to balance all of the state's interests."

Schumer, an increasingly powerful figure in the Democratic party, declined to discuss the selection process.

And with Clinton remaining in office until she is confirmed as Secretary of State, groups will have plenty of time to beg or bluster on behalf of their favored candidate.

Paterson doesn't lose much by waiting, except possibly some peace and quiet over the holidays.

An early resignation and appointment doesn't affect the U.S. Senate's all-important seniority rankings when it comes to committee assignments. Senate Democratic Secretary Lula Davis said that even if a replacement was picked and sworn in next week, that person would be considered no more senior than any of the newly elected senators coming to Congress in January.

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Davenport reported from Phoenix. Associated Press Writer Valerie Bauman contributed reporting from Albany, N.Y.

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