Landrieu has proposed a bill to allow consumers to keep their health insurance plans even if those plans don't meet the standards set by the law.
Several million people who buy insurance on the individual market may get cancellation notices on policies, despite Obama's oft-repeated assurances that people who like their insurance plans would be able to keep them.
The proposal by Landrieu, who is facing a tough reelection fight next year, is meant to undo some of the political damage.
White House officials have said that many of the canceled policies provide very scanty coverage and that many consumers could get better coverage in the new healthcare markets created by Obamacare. Even if that proves true, however, the fact that Obama's repeated pledge has proven false has created a serious political problem for the administration.
On Thursday, Obama apologized to consumers who've received cancellation notices. In an interview with NBC News, the president said his aides were working to fix what he described as "loopholes" in the law, but he did not specifically comment on the Landrieu proposal.
"We're looking at a range of options," Obama said in the interview.
Aides say Obama won't focus on health during his brief stop in New Orleans before heading to three fundraisers in Miami.
On a visit to the Port of New Orleans, the president will boast of his efforts to invest in infrastructure that can boost exports, trade and job creation. Dredging and expansion projects at the port on the Mississippi River has increased exports moving through the region by 140% since 2009, the White House says.