Obama told the senators that he shared their concerns about Americans' ability to access the health insurance exchange and asked for their input on the law's implementation, according to a White House statement on the meeting.
Red state Democrats have expressed worry that poor implementation of Obamacare could negatively impact their re-election chances. Many have called on the president to extend the enrollment period to allow the administration time to fix website glitches.
Begich released a statement after attending the meeting at the White House and demanded that the President address issues with the website immediately.
"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," he said in the statement. "Alaskans should be appreciating the critical benefits of the Affordable Care Act but there is an understandable crisis in confidence because the administration has yet to get it off the ground."
Sen. Ed Markey (D-MA) is also up for re-election in 2014, but was not at the meeting.