If he wins the nomination and then the Presidency, he's likely to be even less successful domestically than Clinton was in his first term. Clinton's budget just barely passed by one vote, Brown's would have so many conflicting elements (like a flat tax rate and a higher corporate tax rate simultaneously) that it probably wouldn't be passed. The government could possibly be shut down while Congress scrambles to draft a budget that satisfies their constituents, their donors, and the wrath of Moonbeam all at the same time. It would be hugely embarasing to Brown and to Democrats generally. From my research on the 1992 campaign, even those close to Brown expected him to be terrible at PR while President. So like Clinton he won't be very persuasive when it comes to advocating for bold policies.
The million dollar question is, does Brown pivot and co-opt GOP policies to get reelected as Clinton did? If yes, then he's projected to win a second term come 1996. If no, then Brown's best hope to stay in office is attacking the GOP Congress and boasting of an improved economy.
Oh, one minor butterfly is that Colin Powell might be promoted to the rank of Five Star General. In OTL, Clinton's team prevented him from getting the promotion possibly due to the fact that he was touted as a GOP challenger in 1996. A different President (not just Brown, it could have been anyone else) might not be so suspicious of Powell - who at the time was not yet politically active - and he might get that coveted fifth star.