Sen. Scott Brown, R-Mass., who is fending off criticism from members of his own party for publicly opposing a GOP plan to overhaul Medicare, could face a potential challenge to his seat from the woman appointed by President Obama to run a controversial agency designed to protect consumers from bank abuses.

Elizabeth Warren, a Harvard law professor who is anathema to Republicans for her fierce criticism of the banks, reportedly is being recruited by Democrats to run for the seat that was held by Ted Kennedy for nearly half a century. Brown surprised Democrats by winning the seat in a special election in January 2010. He is up for re-election in 2012.

Now Democrats want Warren to abandon her role setting up the Bureau of Consumer Financial Protection, a byproduct of the sweeping Wall Street financial oversight law, for a campaign to unseat Brown, who is popular in a reliable blue state.

The Democratic Senatorial Campaign Committee (DSCC) would not confirm that it is wooing Warren to run nor would a spokesman deny it.

Warren hasn't said whether she's interested in running. She went to the Capitol on Tuesday to defend the bureau before the House panel overseeing the Troubled Assets Relief Program. Warren gave a detailed account about the agency's work so far and attempted to bat down criticism, but she wouldn't mention her future plans, saying it would be inappropriate to discuss a potential recess appointment.

Republicans suspect that Obama might appoint Warren to head the bureau when the Senate is in recess next week in response to their threat to block any other nomination until a director is chosen.

Republicans are still smarting over Warren taking on an advisory role to set up the bureau to avoid any contentious Senate confirmation process.

Meanwhile, Brown has earned criticism over an op-ed he wrote objecting to Wisconsin Rep. Paul Ryan's budget plan, which calls for restraints on Medicare spending by giving premium support for seniors to buy private insurance. Democrats have attacked the plan as an assault on the nation's elderly.

In an opinion article published in Politico and entitled "Why I Don't Back Paul Ryan's Medicare Plan," Brown praised Ryan for starting a debate on entitlement spending but said he would vote against his budget.

"First, I fear that as health inflation rises, the cost of private plans will outgrow the government premium support -- and the elderly will be forced to pay even higher deductibles and co-pays," he wrote, adding that the program has already been cut significantly to help pay for President Obama's health care law.

Sen. Kelly Ayotte, R-N.H., a member of the Senate Budget Committee, told Fox News on Tuesday she thinks Brown is missing the big picture.

"I think that there's obviously respectful disagreement here, but I think we can't tweak around the edges here," she said. "We know by 2024, the program is going to go belly up. So we have to make changes to preserve it."

Rep. Joe Walsh, R-Ill, told Fox Business Network that Brown should be "ashamed of himself" for opposing the plan.

"This is the defining moment of this generation," he said. "We have got to be bold. We know these entitlements have to be reformed to be saved. He knows that."

Brown's office did not respond to two emails seeking comment.

Brown isn't the first Republican to face pushback over criticism of the Ryan plan. Former House Speaker Newt Gingrich, who is running for president, was roundly denounced by Republicans for calling the Ryan plan "right-wing social engineering."

Democrats have seized on both of their comments. The DSCC has accused Brown of flip-flopping on the Ryan plan.

"Scott Brown has lost his barn coat sheen," DSCC spokesman Matt Canter said in a statement. "He talks like a D.C. politician who is trying to have it both ways and hide his own extreme positions."

Canter added, "There is still so much that Brown is refusing to tell his constituents about where he stands when it comes to Medicare and protecting seniors."