P.S. Saw Juan Williams on Fox this morning. Regardless of NPRs appropriateness, he's clearly better off from the incident. ;-)
Although Paul has never been to Rome, he arguably knows a little about the church there.  In particular, Roman believers seem to have argued over things like meat from pagan temples just like the Corinthians did. In Romans 14-15, Paul labels the two sides in such issues as the "strong" and the "weak." The strong are those whose faith is strong enough to eat meat that has been sacrificed to a pagan god or who can give every day to the Lord without worry (14:1-2). The weak are those who are troubled over the potential uncleaness of their meat or who feel constrained to observe the Jewish Sabbath (14:5).
To be sure, we should take into account the strong possibility that there is an element of rhetoric here. Paul makes the "strong" feel good by putting them in a position of knowledge and strength. But his goal is to lead them to respect and honor those who are more conservative. In a sense, he massages the ego of the person who feels free to do certain things, while moving them in the direction of those who do not.
His argument is very similar to what he said about "disputable matters" at Corinth, although it is more general here in Romans. Paul gives no evidence in this chapter that the debate is a Jew-Gentile one at Rome. Indeed, we have argued throughout the book thus far that Paul's audience in Romans was predominantly Gentile.  We will grow in our thinking about the early church if we recognize the strong likelihood that there were both Jews who were "ultra-liberal" on these issues and Gentiles who were "ultra-conservative" on them.
Although Paul does not bring out the issue explicitly, the eating issue is almost certainly the same question he faced at Corinth--whether a believer should eat meat that has been sacrificed to an idol. In fact, he is writing Romans from the city of Corinth, where their saga was no doubt fresh in his mind. So when he mentions vegetarians (14:2), he is not talking about people who did not believe in killing animals and eating them. He is talking about people who are so concerned about potentially eating meat that had been sacrificed to a god that they preferred not to eat meat at all.
Several items of background are helpful here.  First, we should remember that meat was somewhat of a luxury. Most ancient people only had meat during city festivals, so not eating meat was nothing like the sacrifice it is today. And most of the meat available in a city probably came from nearby temples. Ancient sacrifices did not consume the whole animal.  Even after priests and the family of the sacrificer had eaten to their fill, a good deal of meat would be left over. Since it could not be refrigerated for later, it might easily make its way to the market place...
 Especially if Romans 16 gives greetings to individuals at Rome. However, see the final section of this chapter where we think it more likely that chapter was directed to the churches at Ephesus.
 You'll have to buy the book to hear the argument ;-)
 See chapter 7, "Disagreement and Disorder at Corinth, in the first Paul volume in this series, Paul: Messenger of Grace (Indianapolis: Wesleyan Publishing, 2010).
 The Jewish "whole burnt offering" was unique to Israel.