The Vatican post, considered a plum appointment by Catholics, has been vacant following the departure of Jim Nicholson to become secretary of Veterans Affairs for President Bush's second term. Hyde is a prominent Catholic layman and a leading foe of abortion.
The 80-year-old Hyde is serving his last two years as chairman of the House International Relations Committee under Republican self-term limits. He is expected to announce his retirement this spring after 16 terms in Congress.
The best Republican chance to pick up a Democratic seat in the Senate next year disappeared Wednesday when Sen. Mark Dayton of Minnesota announced he would not seek a second term.
Dayton's approval rating had dropped to 43 percent, and he was far behind in raising money for a re-election campaign after self-financing his previous candidacies. Republicans licked their chops when possible Democratic challengers announced they would not take on Dayton in the primary.
With Dayton out, the Minnesota Senate race becomes a tossup. State Attorney General Mike Hatch is considered the strongest Democratic possibility, but he may run for governor. The leading Republican is Rep. Mark Kennedy, who last November survived a strong Democratic challenge. GOP leaders dread the prospect that former Sen. Rod Grams, beaten by Dayton in 2000, may run again.