You need 60 votes in the senate to pass anything unless you eliminate the filibuster (the so called nuclear option). Obama had 60 Democrats exactly which means if even a single Democrat was willing to vote against a federal right to abortion law Obama couldn't have done it.
First, they only had 59% of the House, not enough to overcome filibuster.
Second, they did have 60% in the Senate, but only for a few months in 2009, and it's not obvious that it was an "overcome filibuster on federal abortion laws" 60%. 2009 was the year Al Franken won a Senate seat in Minnesota after a recount and a Minnesota Supreme Court case, so he wasn't seated until late April. A couple of months later, Ted Kennedy died and was replaced by an interim appointee; Scott Brown, a Republican, won the special election to replace him that winter. They also had Arlen Specter - a Republican - caucusing with them to make that 60. He was a "pro-choice but personally opposed" legislator and may not have voted with the Democrats on this issue.
So yeah, they didn't try. But I think it's very likely they didn't try because they felt strongly that they would not be successful.