FILE - Sen. Patty Murray (D-Wash.) (AP Photo/J. Scott Applewhite)

Sen. Patty Murray (Wash.), an influential member of Democratic leadership, endorsed the Iran nuclear deal Tuesday in a lengthy statement that voiced some doubts of the plan's efficacy but gave a strong overall backing for the outline.

Murray became the 29th Democrat in the Senate to back the plan, with only two Democrats declared in opposition, putting the White House on the cusp of ensuring President Obama can fully implement the pact lifting sanctions on Iran in exchange for limits on its nuclear development.

Obama's opponents need to win over 11 of the remaining 15 Senate Democrats who have not declared their positions on the deal, or else those opposed to it will fall short of the two-thirds majority they need to override the president's veto of their legislation disapproving of the agreement.

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The president's supporters are increasingly confident they can get at least 34 votes in the Senate -- the minimum needed to sustain his veto -- and are now openly talking about getting at least 41 Democrats to back the deal so that the opponents' legislation would be filibustered in the Senate and never even reach the Oval Office.

Noting that she considered this vote akin to her votes authorizing war, Murray said that opponents' push to reject this and "go back to the negotiating table and try to get a better deal" was flawed in its logic.

"I am convinced that moving forward with this deal is the best chance we have at a strong diplomatic solution, it puts us in a stronger position no matter what Iran chooses to do, and it keeps all of our options on the table if Iran doesn't hold up their end of the bargain. I believe that rejecting this deal would continue Iran down the path they are currently on, it would do nothing to stop their short-term ability to develop a nuclear weapon," she said in a statement issued Tuesday by her office.

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Murray is the No. 4 member of the Democratic leadership team, while also serving as the ranking member of the education committee that just won Senate approval of a sweeping rewrite of kindergarten-through-12th grade standards. She served two stints as her caucus's campaign chief, most recently in 2012 when all 25 incumbents facing re-election that election won another term. She is considering a challenge next year to Sen. Richard J. Durbin (D-Ill.), who is the No. 2 member of leadership as minority whip.

Durbin has been the president's point man in the effort to whip support for the Iran deal, running up the score against opponents who originally expected the five-week break to create pressure points back home for senators.

More Senate Democrats are expected to announce their positions in the coming days, and it's possible that Obama will be assured of enough support to sustain his veto before Labor Day weekend.