Particular techniques for NP-complete problems
For such a broad technique as dynamic programming, the answer is almost certainly no. Suppose somebody proves that P&nbsp;=&nbsp;NP (and we don't know that they can't) by giving a polynomial-time algorithm for 3SAT. Surely, that algorithm could be rewritten as some kind of trivial dynamic programming, since pretty much any for loop can be written as dynamic programming.  For example,

total=0
for i=1 to n do
    total = total + data[i]
print total


can be rewritten as

total[n] = data[n]
for i=n-1 downto 1 do
    total[i] = total[i+1] + data[i]
print total[1]


However, one result that is in the spirit of a "yes" answer to the question is in Mihalis Yannakakis's paper "Expressing combinatorial optimization problems by Linear Programs" (Journal of Computer and System Sciences, 43(3):441-466, 1991; DOI, free PDF). This shows that any symmetric linear program for TSP must have exponential size &ndash; a linear program is symmetric if, whenever you permute the main variables, you can permute the auxiliary variables to get back the original program. Yannakakis's paper was, as I understand it, written because Ted Swart had been trying to use linear programming to solve Hamiltonian cycle in&nbsp;P and couldn't quite get the very large ($n^8$ to&nbsp;$n^{10}$ variables) linear programs to work.