The first Democrat has signed on to a House Republican bill that would allow people to keep their current health insurance plans: Rep. John Barrow (D-Ga.).

Barrow announced his support for the "Keep Your Health Plan Act" in a statement Tuesday.

"When folks were first introduced to the Affordable Care Act, they were promised that they could keep their current plan if they liked it," Barrow said.  "As it turns out, that’s not the case today.  ... This bill is the most responsible, bipartisan approach to removing the insurance burdens many will face in 2014, and I’m proud to work with my colleagues to move it forward."

Barrow, who comes from one of the reddest districts held by a Democrat, initially voted against the health-care law and was one of nine House Democrats to back a GOP effort last month to fund the government but delay the individual mandate portion of the law.

The House will vote this week on the new bill, which would allow any health insurance plan that existed before January 2013 to be kept. Eighty-eight House Republicans have co-sponsored the bill.

The health care law allows people to keep any plan that existed before the law passed in 2010, but its standards have forced many plans purchased on the individual marketplace since then to be canceled because they don't qualify.

Despite this, President Obama claimed repeatedly in recent years that people who liked their insurance plans could keep them under the new law.