“I, as you know, have great fondness and great respect for Sen. Clinton and I’m very loyal to her,” Feinstein said. “Having said that, I’d like to talk with her and [get] her view on the rest of the race and what the strategy is.”

“I think the race is reaching the point now where there are negative dividends from it, in terms of strife within the party,” Feinstein said. “I think we need to prevent that as much as we can.”

Tuesday night’s results are widely viewed as a blow to Clinton’s hopes after she failed to deliver a “game-changing” performance. Instead, Obama extended his leads among delegates and popular votes.

Feinstein stressed that Clinton is not an “also-run candidate,” but added that there is a question “as to whether she can get the delegates that she needs. I’d like to see what the strategy is and then we can talk further.”

Senate Majority Leader Harry Reid (D-Nev.) repeated Wednesday that he wishes to remain neutral in the race and the  superdelegates should make up their minds shortly after the final primary on June 3.

 As for whether Clinton has a reasonable path forward, Reid said this: "That's not for me to judge. She has her campaign going. Obama has his going. I'm not going to be running campaigns."

Other Clinton Senate supporters sounded more optimistic and stressed the high voter turnout as a positive for Democrats.

Sen. Barbara Mikulski (Md.) said Clinton is a “fighter” and rejected the suggestion that she should quit.

“The voters aren’t sick of it — look at all the record turnouts,” Mikulski said. “It’s helped the party.”

Sen. Evan Bayh (Ind.) said the tight race is not harmful to the party but warned that the contest between the two heavyweights should not become “bitter and personal” as it wraps up.

Meantime, several other Senate Democrats said Wednesday that they are detecting a shift in the race between their colleagues.

Sen. Jack Reed (R.I.), who remains uncommitted, said Tuesday night’s primary results “shifted momentum” in the contests.

Sen. Frank Lautenberg (N.J.), who also has not endorsed a candidate, stated that “the hill has gotten steeper” for the former first lady.

Obama supporters echoed the sentiment while being careful not to push Clinton out of the race. “It was an extraordinary win and a magnificent campaign,” said Sen. Edward Kennedy (Mass.). “I pay tribute to Sen. Clinton. She’s been making her case and doing it effectively, but the outcome is very clear for the Democratic nomination. It’s effectively Barack Obama's nomination.”

Sen. Byron Dorgan (N.D.) said Clinton would have to “make her own decision.”

“Both are colleagues — they have run aggressive campaigns … but ultimately, there is going to be a winner,” Dorgan stated. “I think last night perhaps moved Sen. Obama closer to that position.”

J. Taylor Rushing contributed to this report.