One line I'm seeing from advocates of the Grand Bargain is that a smaller deal to lift the debt ceiling won't be any easier:

Mr. Obama is pushing for a bigger deal on the argument that it will, paradoxically, be easier for Democrats and Republicans to sell to their rank and file, because they could present it as a historic effort to begin undoing years of deficit spending.
As Mr. Geithner said on “Face the Nation,” “It’s not clear that it’s easier trying to do less.”

I suppose it's true that you can more easily get members of Congress to sacrifice their priorities if they think they're supporting a historic deficit deal to end all deficit deals rather than the first fiscal adjustment in a series. But every previous fiscal adjustment since Ronald Reagan introduced massive peacetime deficits has been incremental -- under Reagan in 1982 and 1983, George H.W. Bush in 1990, a Bill Clinton in 1993, and Obama's Affordable Care Act in 2010. the history has always been taking bites out of the deficit problem one at a time, rather than reordering the federal budget in a big bang.

In any case, the Republican anti-tax animus appears insurmountable. The only deal that seems plausible to me is one that would be scored as having no net tax increase but still would raise revenue as compared with current law. The medium deal is where it's at.