That's according to the results of a poll conducted by the Mercyhurst Center for Applied Politics at Mercyhurst University in Erie, PA that were released Monday.
The poll included 425 registered republicans in Pennsylvania.
The results show former Pennsylvania Senator Rick Santorum still has a slight lead in The Commonwealth, but is losing that lead to Mitt Romney.
If the primary were held today, 37% of the state's registered republicans would vote for Rick Santorum.
31% would vote for Mitt Romney.
One month ago, polls showed Santorum up by 20 points.
Now, despite that, the poll found the majority of republicans still think Romney has a better chance of beating President Obama in the November General Election than Santorum does.
"We're probably seeing something that's not uncommon in the republican primary contest and that is Mitt Romney tends to come on strong towards the end and that may in fact be what's happening here," said Dr. Joe Morris, Mercyhurst Center for Applied Politics.
As part of the poll, the registered republicans were asked to choose one word to describe each of the four candidates for President.
For Romney, the most frequent words chosen included businessman, moderate, rich and arrogant.
For Santorum, those words most frequently chosen were relatively positive and included honest, moral, good and conservative.
Dr. Morris said, "I think this says something about how Pennsylvanians are perceiving these candidates. Rick Santorum has gone to great lengths to portray himself as a conservative alternative to Mitt Romney and the results of our poll suggest this seems to have been fairly effective, he's done a good job at this."
When it comes to the issues, many of the republicans polled said, to them, the economy was either the first or second most important issue in this primary election.
Health care was also of primary or secondary importance to more than 100 persons polled.
The poll results will be posted on MCAP's website in the coming days.