House Republicans are out today with a baroque proposal on the debt limit. Rather than allowing the federal government to continue financing previously authorized spending by increasing the debt ceiling, they would leave the ceiling where it is but "suspend" it until May 19. In addition, they would include a gimmicky "no budget, no pay" provision that says members of the Senate will have their pay cut unless they pass a budget.
In practice, it shouldn't be hard for Senate Democrats to pass a budget. They haven't passed one in recent years because, given the partisan gridlock in recent years, the budgeting is de facto done through measures like the Budget Control Act and last-minute deals to avert government shutdowns. Given that, there's no substantive purpose served in passing a budget, and senators haven't wanted to open themselves up to attack ads accusing them of having voted for such-and-such deficits or such-and-such tax hikes. Ducking budget votes, however, has become a GOP talking point all of its own. Democrats can respond with a budget resolution that calls for some fairly hazy revenue-increasing tax reform measures and call it a day.
That said, there's a good case that "no budget, no pay" rules are unconstitutional under the 27th amendment. No sitting Congress is allowed to raise or cut its own pay, only the pay of future Congresses.
The GOP theory is that the provision would only suspend members' pay until the passage of a budget and not actually cut it. That sounds like a distinction without a difference to me, and certainly you could launch a plausible lawsuit around it. My view is that it would be strongly preferable to avoid injecting legal uncertainty into the debt ceiling situation, especially legal uncertainty that's not really about anything. What's needed here isn't a "no budget, no pay" rule in the debt ceiling bill, it's an agreement between congressional leaders. John Boehner has to agree to lift (or "suspend") the debt ceiling, and Harry Reid has to agree that Senate Democrats will write and pass a budget, exposing themselves to GOP criticism over their tax and spending plans.* That way, the debt apocalypse will be reverted, Republicans can say they forced Democrats to pass a budget, and Democrats will be held accountable by the public for their fiscal vision.
* Correction: This post originally suggested that Mitch McConnell should agree not to filibuster the Democrats' budget resolution. Senate rules don't allow for filibusters on budget resolutions.