A new Iran sanctions bill is gaining momentum on Capitol Hill as talks to finalize a nuclear deal drag on between the Obama administration and Iranian officials.

Fifty-nine senators have signed onto a bill introduced by Foreign Relations Committee Chairman Bob Menendez, D-N.J., and Sen. Mark Kirk, R-Ill., up from 33 co-sponsors in late December.

One Senate aide though said the bill had reached a veto-proof majority – well above 67 and into the 70-vote range, referring to whip counts of those planning to back the bill if it comes to the floor for a vote.

Democratic leaders have so far blocked a vote on the bill, but Senate Majority Leader Harry Reid, D-Nev., in December put the bill on the official Senate calendar.

Senate aides say they expect the vote to come during the first week of February after President Obama delivers the State of the Union address Jan. 28.

The Obama administration has said it would veto a new sanctions bill and has pleaded with Congress not to push a new round, saying any movement on the legislation could jeopardize delicate negotiations with Iran.

But senators pushing additional sanctions are defying administration warnings. They say Iran can't be trusted to abide by its commitments and the threat of new economic pressure strengthens the administration's hand and gives U.S. officials more leverage to finalize the deal and start its six-month clock.

The bill started attracting more sponsors in early January after reports that negotiations between Iran, the U.S. and five other world powers implementing the deal had hit a snag over advanced centrifuge research. Lawmakers were reacting to reports that Iran planned to move forward with developing an advanced nuclear centrifuge that would purify plutonium in a more efficient way.

“That means this entire [diplomatic] process has not changed their ultimate goal – they're still trying to break out and develop nuclear weapons,” said a Senate aide.

Several prominent Democrats signed onto the bill this week, including Sen. Michael Bennet of Colorado, who chairs the Democratic Senatorial Campaign Committee, the political arm charged with maintaining the Democratic majority.

Democrats' willingness to break with Obama on the issue demonstrates the party's lingering frustrations about the botched rollout of Obamacare, as well as a growing distrust of the administration's Middle East foreign policy and officials' ability to extract lasting concessions from the Iranians.

“A lot of Democrats we're talking to say we have no favors to give Obama right now,” the Senate aide said. “And when the [administration] says just give us some slack and help us out on this one – they're not inclined to do that.”

Menendez and Kirk have argued that the measure would not impact the negotiations because it gives Obama more than a year to continue diplomacy before any new sanctions would kick in. While providing some initial relief, the administration has continued to keep most existing sanctions against Iran in place and they would intensify if Iran violates any part of the interim deal.

Secretary of State John Kerry first announced a historic deal with Iran in late November that would place new limits on Tehran's nuclear development. But senators have complained that the process of finalizing the six-month interim deal has dragged on.

Iran's nuclear envoy in Geneva said Friday that an initial agreement has been reached but State Department spokeswoman Jen Psaki later said reports that “everything has been finalized” are incorrect and the talks are still ongoing.

“These are detailed, technical discussions,” she said. “We've made good progress over the last several days. There have been a few outstanding issues.”

This story was published at 3:38 p.m. and has been updated.