Enough Tea Party-supported candidates are running strongly in competitive and Republican-leaning Congressional races that the movement stands a good chance of establishing a sizeable caucus to push its agenda in the House and the Senate, according to a New York Times analysis.

With a little more than two weeks till Election Day, 33 Tea Party-backed candidates are in tossup races or running in House districts that are solidly or leaning Republican, and 8 stand a good or better chance of winning Senate seats.

While the numbers are relatively small, they could exert outsize influence, putting pressure on Republican leaders to carry out promises to significantly cut spending and taxes, to repeal health care legislation and financial regulations passed this year, and to phase out Social Security and Medicare in favor of personal savings accounts.

Still, the bulk of the Tea Party candidates are running in districts that are solidly Democratic, meaning that most Tea Party efforts — no matter how energetic — are likely to register as basically a protest vote.

An analysis of each House and Senate race found 138 Tea Party candidates, all Republicans, running for nearly half the Democratic or open seats in the House and a third of those in the Senate — or, in the case of two Republican House incumbents, defending seats won with Tea Party backing in special elections earlier this year.

Tea Party nominees have performed better than expected in many cases, including races in which the establishment candidates they defeated in the primaries were considered the stronger general election contenders. This includes well-known nominees like Rand Paul, running for the Senate in Kentucky, as well as lesser-known candidates like Dan Benishek, running to replace a retiring House Democrat in Michigan.

But as establishment Republicans feared, the Tea Party has also handed opportunities to the Democrats by nominating candidates who have struggled.

Of 129 Tea Party candidates for the House, 7 are running in solidly Republican districts — all but one of those seats is now held by a Republican. Another 7 are running for seats currently held by Democrats but in districts leaning toward the Tea Party Republican.

Nineteen are in tossup races, for seats that are held, with the exception of two, by Democrats. And 29 are running for seats in districts that are leaning Democratic — of those, only one is currently held by a Republican. Sixty-seven are challenging Democrats who are expected to win — though this is a year when the unexpected has been more rule than exception.

In the Senate, there are 9 Tea Party candidates running for a potential of 27 seats — not including those where the incumbent is the Republican nominee.

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(Read More: NY Times)