Karen Bradley is appearing at the Northern Ireland Affairs Committee.
The DUP's Sammy Wilson had accused the groups of being "puppets for the Northern Ireland Office".
Strangford MP Jim Shannon told her: "If you don't cast your net wider and seek opinions of other people and stop seeking the... one blinkered opinion, which it is clear to me that some people are pursuing, then you are going to get a very rude awakening".
He also said the DUP's view was that in the event a backstop came into effect, it would not be a short-term arrangement, and therefore his party would not be supporting the deal in the Commons.
The backstop would force Northern Ireland to align with Brussels' single market rules, and keep the Irish border open.
Ms Sturgeon also reportedly met the Prime Minister, who is losing support for her deal, with member states threatening to block it in Europe and both Brexiteers and pro-EU politicians voicing criticism in the United Kingdom parliament.
The move throws into doubt the future of the confidence and supply arrangement that sees the DUP's 10 MPs vote with the government.
"Following discussions between [the DUP and the Conservatives], and in order to support their shared objectives of strengthening the economy, the UK Government is prepared to make available additional financial support to the power-sharing executive". But on Monday, the DUP abstained on the first two votes on the Finance Bill, and eight DUP lawmakers voted against the government in a third vote, on an amendment to the bill proposed by the opposition Labour party.