The president should declare that he would sign a bill that contains substantial additional budget cuts -- but only if it sets a trigger that activates them automatically after the unemployment stays at or below 7 percent for six months.
One can set the unemployment rate at some other figure (say, 7.25 percent) or the trigger period at some other interval (three months?), but the main features must remain: the recognition that (a) additional budget cuts at this point may stall the economic recovery; (b) unemployment is unacceptably high; (c) as the economy grows stronger, we must attend to the deficits in earnest; and (d) the president is irrevocably committed to attending to both jobs and deficit-cutting.
One may quibble and ask: what if there is some great disruption? Say, oil prices rise to $200 a barrel or... or... Congress of course could reverse itself, but the president should sign such a bill as soon as it reaches his desk.
Note that according to a February 2011 Gallup poll, 35% of Americans felt unemployment was the most important problem facing America; only 11% said the same of the deficit. Another February poll conducted by Pew found the same trend. 44% of Americans said the job situation was the economic issue that worried them most, while 19% said the deficit worried them most.