Senate Budget Chairman Kent Conrad (D-N.D.) won’t unveil his budget to the public this week after all, aides said Thursday.

Conrad had said earlier in the day that the timing would be decided by Senate Majority Leader Harry Reid after the Nevada Democrat and other Congressional leaders attended a morning meeting at the White House about raising the debt limit and reducing the deficit.

Keeping the budget under wraps may be a sign of progress in the larger debt talks. That’s because the Democratic budget plan is just for show — there are no plans yet for a markup or to bring the plan to the Senate floor. Even if Democrats did move forward with the measure, they probably wouldn’t have the votes for passage in the Senate, and the proposal would be dead on arrival in the Republican-controlled House.

Conrad acknowledged that a handful of Democrats may not support his plan. But with just 53 Senators caucusing with the Democrats, a handful of defectors would be enough to sink it.

Sen. Ben Nelson, who is up for re-election in 2012, said he could not vote for the Conrad budget as it was presented to him because it assumes large revenue increases. The Nebraska Democrat said the focus of debt talks needs to be spending cuts, not taxes.