Hillary Clinton was under pressure to do well in Democratic nominating contests in Kentucky and Oregon so she can turn her attention to the general election and the mounting attacks on her by Republican candidate Donald Trump.
The continued presence in the race of Bernie Sanders — who remains a long-shot to upset Clinton and win the Democratic nomination — is prompting concerns among her allies that he will damage her ability to take on Trump and hurt the Democrat in the autumn.
But supporters of Sanders shrug off that worry, arguing Trump is such a flawed candidate that Clinton will easily defeat him if she faces him in the November 8 election.
Supporters said that Sanders should keep fighting until the Democratic National Convention in July, to push Clinton to the left and challenge her ties to Wall Street and support for free-trade deals.
Allies of Clinton have held back from overt calls for Sanders to exit the race.
Moves by her campaign to try to push him out could risk angering Democratic voters .
The Democratic race is unlikely to wrap up before California, New Jersey, and several other states vote on June 7.
Oregon, with a heavily white, liberal population, politically resembles its northern neighbour Washington, which voted for Sanders.
Oregon voters cast their ballots by mail, meaning voting there actually began in the last week of April.
After Sanders won both West Virginia and Indiana this month, analysts said he has a good chance of taking Kentucky.
Louisville and the western part of the state are more moderate politically, and Clinton spent Sunday and Monday campaigning there.
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