Senate Budget Chairman Kent Conrad’s (D-N.D.) decision to present a budget plan to the public this week — but not vote on it — is fraught with risks for the majority, aides in both parties say.

Democrats have avoided bringing a budget to the Senate floor for the past two years in part because doing so exposes their Members to unlimited, unpredictable amendment votes — and because a budget is a nonbinding resolution that does little beyond setting internal spending levels or serving as a party platform.

That’s especially true this year, when any partisan budget would be dead on arrival in the Republican-run House.

Having a budget this year would also present a problem because, while the public likes deficit reduction generally, almost every specific plan to do so includes unpopular elements.

However, Conrad and other Democrats on the Budget Committee said their plan could provide ideas and an alternative vision for the bipartisan deficit talks — especially given that various efforts to reach a deal have stalled.

Sen. Bernie Sanders (I-Vt.), a member of the Budget Committee, said Tuesday that Democrats and the president should get behind a strong alternative to Republican proposals that would cut various government programs for the middle class and the poor.

“The vast majority of the people are behind us, and they have got to know that some of us are fighting for what they want. … I think the American people want to hear an alternative,” Sanders said.

Sanders sent a letter to President Barack Obama telling him not to yield to the GOP, and he told reporters that Obama has not done a good enough job fighting for progressive priorities.

“He has got to stand tall and say to the wealthiest people in this country, ‘Sorry, you have got to be part of deficit reduction. We’re not going to throw millions of kids off Medicaid health insurance and not have you contribute a nickel,'” Sanders said.

But several senior Senate Democratic aides questioned the wisdom of proposing a Democratic budget, especially so long after the April 15 deadline.

“It doesn’t mean anything,” one aide said, noting that the only thing that matters is bipartisan negotiations on the debt limit.

Indeed, it could get in the way of the party’s message, they said.

Democrats feel they have gotten some momentum by putting Republicans on the defensive on tax breaks for the rich and for assorted luxuries such as corporate jets, yachts and racehorses. But a far more ambitious Democratic budget plan calling for perhaps $2 trillion in tax increases over the next decade — something more ambitious and liberal than Obama himself has outlined — would give the GOP a fat target to shoot at, just as Democrats have successfully tarred Republicans with House Budget Chairman Paul Ryan’s (R-Wis.) Medicare plan.

Another problem that could prove embarrassing for Democrats: Under Senate rules, any Senator can bring a budget resolution to the Senate floor if the majority has failed to do so after May 15.

Therefore, Republicans could force Democrats to vote to proceed to their own budget whether the majority wants to or not. Senate Minority Leader Mitch McConnell (R-Ky.) already used the maneuver when he forced a vote on Obama’s budget earlier this year.

Democrats would be in a position of either rejecting their own budget or — perhaps even worse for them — voting to take it up and having their sizable contingent of vulnerable incumbents face an onslaught of politically charged amendments.

Several aides said they wouldn’t be surprised if Conrad ultimately holds off on presenting his plan after briefing leaders and the rest of the Democratic Conference on it today.

In the meantime, Senate Majority Leader Harry Reid (D-Nev.) gave up Tuesday on his plan to proceed with a resolution authorizing U.S. military involvement in Libya after Republicans objected. GOP Senators argued that the reason for canceling this week’s recess was to deal with the budget and the debt limit.

Republicans, led by Sen. Ron Johnson (Wis.), said they would object to any legislation not dealing with the debt and the budget until the matter is settled.

“The Senate is basically fiddling while America goes bankrupt,” Johnson said during a hastily called Tuesday afternoon press conference.

In lieu of the Libya resolution, Reid on Tuesday filed a motion to limit debate on his nonbinding resolution calling for people making more than $1 million a year to contribute to deficit reduction.

The measure is intended to highlight Democrats’ call for the elimination of tax breaks for the wealthy, but the Sense of the Senate resolution does not propose any specific tax changes. Still, Democrats are considering holding votes on the variety of tax breaks they spotlighted last week.

The GOP will have its opportunities to put Democrats on the spot, too.

“They better be careful what they wish for on this,” a senior GOP aide said.

And McConnell noted that taxes on luxury items such as yachts backfired in the early 1990s, when thousands lost their jobs before the tax was rescinded.

Obama, for his part, invited leaders from both chambers to the White House on Thursday and said he wants a deal on the debt in the next two weeks.

He rejected talk of a short-term deal that Republicans have been floating as of late.

“I don’t think the American people sent us here to avoid tough problems. … We’ve got a unique opportunity to do something big,” he said.

He continued to insist on a “balanced” approach that includes eliminating tax breaks for the wealthy and corporations.

David Drucker contributed to this report.