The best news is for Giffords. The poll, which has a margin of error of 4 percentage points, showed Giffords favored by 44.7 percent of likely Democratic voters. Her closest rival, former Tucson news anchor Patty Weiss, garnered 26.7 percent support. Some 20 percent of Democratic voters remained undecided.

In the largely three-way Republican race, Graf leads with 35.7 percent of the vote, more than 22 percentage points ahead of his closest rival. But 39 percent of voters in that contest said they still had not chosen their candidate.

Perhaps the biggest surprise in the poll is that despitea more than $200,000 money advantage over Graf, an endorsement by retiring Rep. Jim Kolbe, and three large advertising buys on major television channels, former state Rep. Steve Huffman, Graf's closest rival, was favored by just 13.3 percent of Republican voters. Mike Hellon, a former Arizona GOP chairman who has aired immigration-related ads on cable TV, was close behind with 10 percent support.

The poll also noted that Iraq and immigration will be flashpoints in the competitive race. Some 60 percent of Republicans said immigration was the most important issue in the election, while almost 40 percent of Democrats cited Iraq.