If you're comparing the correlation of two variables, just report the Spearman correlation coefficient. The Spearman correlation is recommended over Pearson correlation for this type of data: How to choose between Pearson and Spearman correlation?.
If you want to know how multiple variables impact the answer to one of the binary questions, do a logit or probit model. I've never used SPSS, but I'm sure there's a menu option for it. Select the binary answer as the dependent variable in the model.
First off, are your two independent variables being adjusted as factors or numerically coded responses and is there an interaction term for the two? The reason I ask is because the test of proportional odds grows very sensitive with small cell counts. For this reason, I often find it justifiable to adjust input variables as their ordinally coded values (1: poor, 2: fair-to-poor, etc.). Doing so allows information to be borrowed across groups, proportionality is assessed so that an associated difference in the odds of a more favorable response comparing units differing by 1 in the predictor are consistent with odds of an even more favorable response (the rough and contrived interpretation of the test of proportional odds).
If your numeric coding still fails to give valid proportionality, it is possible to get consistent cumulative odds ratios estimates by collapsing adjacent categories like the two bottom box responses.
Thirdly, another powered test of association between an ordinal response and two ordinal factors is a plain old linear regression model. Using robust standard errors, you get valid confidence intervals despite the distribution of the errors. This tends to be less powerful that categorical methods, but with fewer pitfalls due to zero cell counts.
Lastly, as a comment, robust standard errors allow consistent estimation of the mean model in most circumstances. I'm not sure if these are implemented in SPSS, but R and SAS use these frequently. As with the proportional hazards assumption in the Cox model, when this "model based assumption check" fails, it does not mean the model results are entirely invalid, it's just that the effect estimates are "averaged" over their inconsistent proportionality. For instance, if proportional odds model has excessive numbers of respondents giving top box responses, and a predictor shows a large association for the top box response but smaller association for other cumulative measures, then you'll find that the cumulative odds ratio is a weighted combination of the several thresholded odds ratios, with a higher weight placed upon the top box OR.
Best Answer
Categorical variables, whether nominal or ordinal, should be recoded to dummies for use in ordinary regression. (The STATS CREATE DUMMIIES or Data > Create Dummy Variables extension command can do this for you conveniently, although with only three known value, COMPUTE would be adequate.) Or you could use GLM, which understands factors.
It does not matter for OLS whether these are considered nominal or ordinal. However, if you have the Categories option, Analyze > Regression > Optimal Scaling can find an optimal scale for your categorical variables in a regression.