A Massachusetts Democrat considered a top prospective Senate candidate said Tuesday that President Obama "may not be" the party's best candidate for president in 2012.

Rep. Michael Capuano (D-Mass.) said that he doesn't think it's useful for Obama to face a primary challenger in his reelection effort, he opened the door to possibly backing another candidate in a primary.

"I don't live in an ivory tower," Capuano said on Fox News. "I have to pick the best amongst those people who are running, and it may or may not be President Barack Obama's reelection."

Capuano is the second senior Democrat to express reservations about the president's leadership in the wake of a deal on tax cuts that many liberals view as a disappointing concession to the GOP. Rep. Joseph Crowley (D-N.Y.) said it's "premature" to say whether Obama deserves a primary challenge, though Crowley's office emphasized on Tuesday that the New York Democrat supports the president.

The murmurs about a primary challenge underscore the anger on the left toward an Obama White House that's viewed as having conceded too much territory to Republicans on a number of issues.

Obama dismissed some of the complaints from liberals in a press conference on Tuesday meant to sell his new tax package. The president warned liberals against being "sanctimonious" about their positions.

Capuano ran for Senate in 2008 and is seen as a possible -- if not probable -- candidate to run again in 2012, when Sen. Scott Brown (R-Mass.) is up for reelection. He said on Tuesday that a primary challenge to Obama might not be warranted -- yet.

"At the moment I don't see that as a useful tool, but I hope the president re-finds his footing," he said.

"By the way, I'm not running for president either," Capuano added.