(Adds quotes from Obama at fundraisers)

By Steve Holland and Roberta Rampton

WASHINGTON/DALLAS, Nov 6 (Reuters) - President Barack Obama met on Wednesday with frustrated Senate Democrats, some of whom fear the disastrous rollout of his signature healthcare law could complicate their already difficult re-election fights in 2014.

The Obama administration has faced intense criticism since hundreds of thousands of people had their health insurance policies canceled because the plans do not meet new benefit requirements, despite Obama's pledge that Americans could keep their current plans under Obamacare.

The fallout has been exacerbated by the fact that those affected cannot shop easily for insurance alternatives on the malfunctioning website, HealthCare.gov.

Obama, joined by Vice President Joe Biden, sat down with 16 Senate Democrats, 15 of them who are up for re-election next year, many of them facing competitive races.

One of the senators, Mark Begich of Alaska, said he expressed his frustration at the website during the two-hour session. It has not worked properly since going live on Oct. 1.

"It's absolutely unacceptable in this day and age that the administration can't deliver on the promises it made to all Americans because of technical problems with a website," Begich said.

Senate Mark Pryor of Arkansas said after the meeting, "The American people are frustrated with the White House's botched rollout of the Affordable Care Act, and I am too." Pryor said he wants Obama to hold "individuals in charge" accountable for the launch.

The meeting came just before Obama left for Dallas to speak at two fundraisers for the Democratic Senatorial Campaign Committee.

Obama told donors that 2014 congressional elections would be a tough fight.

"The math is difficult for the Senate," Obama said. "If we don't give them the help that they need, then we could end up with a situation in which we've got a majority Republican Senate along with a majority Republican House."

In a sign of its political potency, the rocky launch of Obamacare appeared to help Republican Ken Cuccinelli cut into the lead enjoyed by Democratic Party insider Terry McAuliffe, who won Tuesday's election for Virginia governor.

'GOING TO GET THIS DONE'

Some of the senators have said they want the enrollment period extended beyond March 31. But Obama believes there is enough time to fix HealthCare.gov and get people enrolled, White House spokesman Jay Carney told reporters.

"We'll be able to do that within the six-month enrollment period that we talked about," Carney said aboard Air Force One.