Here’s a link to the many stories at HuffPost about this issue.

Tim Geithner:

14th Amendment says debt shall not be questioned. 

Sen. Chuck Grassley (R-Iowa) said on Thursday

…that the Constitution may trump the debt ceiling, allowing the administration a way out of the default impasse. 

Rev. Chuck Currie:

Invoking 14th Amendment A Moral Option To Solve Debt Ceiling Impasse 

Jennifer Bendery at HuffPost writes:

“We believe that the president should invoke the 14th Amendment,” Rep. Eliot Engel (D-N.Y.) said Wednesday. “The debt ceiling must be lifted,” said Del. Donna Christensen (D-Virgin Islands), also at the press conference. “And if that is the only way to get it done, then Mr. President, do it. And we and many more Members will stand with you.” Other Democrats, including Reps. Jerrold Nadler (N.Y.), John Garamendi (Calif.) and Sheila Jackson Lee (Texas), are also calling on Obama to step in to resolve the debt crisis if Congress can’t reach a deal by August 2, when the government is expected to run out of money to pay its bills and begin to default. “Our president, we believe, has the [ultimate] power to solve this,” Garamendi said. “We hope he doesn’t have to use it.”[snip]
The provision at the heart of the constitutional debate, Section 4 of the 14th Amendment, states: “The validity of the public debt of the United States, authorized by law, including debts incurred for payments of pensions and bounties for services in suppressing insurrection or rebellion, shall not be questioned.” Essentially, Democrats are arguing that since the “public debt” cannot be questioned, then the debt ceiling itself is unconstitutional.[snip]
“I am convinced that whatever discussions about the legality of that can continue,” Assistant Minority Leader James Clyburn (D-S.C.) said. “But I believe that something like this will bring calm to the American people and will bring needed stability to our financial markets.”[snip]Engel speculated that Obama’s resistance to the option may fade if it becomes apparent that Congress can’t reach a deal by August 2.

Reuters:

President Barack Obama says he will not bypass Congress and cite an obscure part of the U.S. Constitution to prevent a government debt default, but legal experts say it would prove difficult to challenge him in court should he change his mind.

Former President Bill Clinton argued last week that the 14th Amendment that states the “validity” of government debt ”shall not be questioned” means that Obama could simply ignore the congressionally imposed debt ceiling and go on borrowing.

Jim Abrams at HuffPost: Democrats say Obama should invoke 14th Amendment

Rep. Xavier Becerra of California, the assistant caucus chair, said Democrats are telling Obama, “Mr. President, Republicans through their failure have given you license to do whatever it takes to not let the American family go down into that abyss with House Republicans.”

Ryan Grim & Samuel Haass at HuffPost:

14th Amendment: Democratic Senators See Debt Ceiling As Unconstitutional 

Jay Weston at HuffPost:

For God’s Sake, President Obama, Invoke the 14th Amendment and End This Madness in Washington 

Paul Abrams at HuffPost:

Constitution Prohibits ‘Deadbeat Nation 

Reuters:

President Barack Obama says he will not bypass Congress and cite an obscure part of the U.S. Constitution to prevent a government debt default, but legal experts say it would prove difficult to challenge him in court should he change his mind. 

Sam Stein at HuffPost:

Gibbs Accuses Senate GOP Of Playing Politics With 14th Amendment Campaign 

There are many more quotes… feel free to read them at this link!