U.S. Rep. Gabrielle Giffords, D-Ariz., is shown at left before she was wounded in a January shooting, and during her recovery in May at right.

WASHINGTON — The shooting of Rep. Gabrielle Giffords in January has left Democrats in Arizona without a candidate for next year’s U.S. Senate race even though party officials in Washington have declared the state a tremendous opportunity to pick up a seat.

Giffords would be the unquestionable favorite to represent the Democrats if she were able to run. As she undergoes therapy to recover from the January shooting, an alternative candidate has yet to emerge — in part, because of the uncertainty surrounding her political future.

“All of our hopes and faith were geared towards her,” said Andrei Cherny, chairman of the Arizona Democratic Party. “Because of what happened in Tucson, I think people are now thinking through the decision themselves.”

Some Democrats said the lack of an alternative at this stage is a worrisome sign that Democrats won’t field a strong challenger against the GOP nominee, most likely to be Republican Rep. Jeff Flake. Incumbent Republican Jon Kyl is retiring after three terms in the Senate.

“We’re stumbling around with names nobody knows,” said Rep. Raul Grijalva, D-Ariz. “We’re left with second tiers, and that’s too bad, because I don’t think Flake should have a free ride and he’s beatable.”

Grijalva said he believes that time is drawing near for the Giffords camp to say whether she will run for the Senate. He made clear he had no intentions of seeking the seat.

“There has been a deference and I think appropriately so,” Grijalva said. “Now, I think it’s kind of important to find out what their decision is going to be, because the more time that goes by, the lower the tier of candidates gets. Formidable people are going to defer to Gabby.”

Privately, some Democrats are pessimistic that her recovery will progress to the point she will run for the Senate.

They view a run for her congressional seat as a more likely alternative.

Jim Pederson, the former chairman of the Arizona Democratic Party, said Giffords has plenty of time to decide and could win the Senate race even if she waited until 2012 before entering.

Pederson acknowledged that her possible candidacy may be scaring off other Democratic candidates.