This post has been updated.

Senate Republicans launched an aggressive push to amend the U.S. Constitution to require a balanced budget Wednesday, insisting that the federal government cannot get out from under crushing debt without one.

In a series of speeches on the Senate floor and a morning news conference, they injected the new demand into talks with the White House on raising the nation’s legal borrowing limit. They promised to make the need for an amendment a major theme this week and next, when senators will return to their home states and talk up the idea to constituents.

“We think it’s pretty clear, regardless of what we’re able to negotiate here in the short term, that we should put the federal government in this kind of fiscal straightjacket, so that we do not get in this position again,” said Senate Minority Leader Mitch McConnell (R-Ky.)

Polls show that a balanced budget amendment is broadly popular. It is also an article of faith for much of the conservative base, and the Republicans’ new emphasis on its passage may be designed to show activists that they take the issue seriously, on the eve of tough compromises on the debt issue.

But the measure has no chance of finding support with Democrats who control the Senate, and it would require spending cuts beyond anything seriously considered so far in negotiations over raising the debt ceiling.

Minutes after the Senate Republicans held their news conference, a group of six Senate Democrats took to the same podium to call on Republicans to support a repeal of ethanol subsidies as part of a debt-limit deal.

“The subsidies, special giveaways, loopholes: Ethanol is the poster child for what’s wrong with Washington,” Sen. Richard Blumenthal (D-Conn.) said at the news conference. “And ending this subsidy will not solve the budget problem alone, but it is a start and a necessary beginning for ending the special breaks for special interests that riddle the tax code and the budget.”

The Democrats -- Blumenthal and Sens. Charles Schumer (N.Y.), Barbara Mikulski (Md.), Sheldon Whitehouse (R.I.), Ben Cardin (Md.) and Robert Menendez (N.J.) -- pointed to the fact that 34 of 42 Senate Republicans voted to eliminate $6 billion in ethanol subsidies earlier this month.

“This is not a question of being for it before you were against it,” Whitehouse said. “This is a question of being for it and against it at the same time. And if we can resolve that discrepancy on ethanol, there’s no reason that we shouldn’t go forward on oil and gas subsidies at a time when the oil and gas companies are making the biggest profits in history.”

House Speaker John Boehner (R-Ohio) has repeatedly said that any debt-limit deal that includes tax increases would not be able to pass the House. Senate Democrats took issue with that point Wednesday, arguing that Boehner will need the support of some Democrats in order to pass an eventual debt-limit deal because a significant number of Republicans have now indicated they won’t vote to raise the debt ceiling.

“For Speaker Boehner to say, as was mentioned before, that he doesn’t have the votes for it -- well, he doesn’t have the votes if he doesn’t have revenues, because he’s not going to get Democratic votes without revenues and he doesn’t have enough Republican votes on his own to pass it.”

Though all 47 Republican senators have said they support a balanced budget amendment, only 12 have signed a pledge, authored by conservative advocacy groups, not to vote to raise the debt ceiling without one.

Lawmakers have been searching for about $2 trillion in savings as part of a debt-reduction package that could lure votes to raise the nation’s legal borrowing limit. They are racing against an Aug. 2 deadline, when the nation could begin defaulting on its obligations without an increase in the debt limit.

To propose a constitutional amendment for ratification, two-thirds of both houses of Congress must agree.

McConnell characterized the amendment as a “good first step” toward achieving long-term budget stability. The effort is also designed to show unity among Senate Republicans. Their news conference was spearheaded both by party veterans and by tea party favorites.

“We will never surmount our fiscal problems until we amend the Constitution,” said Sen. Rand Paul (R-Ky.). He has said he will oppose a debt deal that does not include a balanced budget amendment.